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Refinar búsquedaAn Introduction to the Heisenberg Group and the Sub-Riemannian Isoperimetric Problem / Capogna, Luca (2007)
Título : An Introduction to the Heisenberg Group and the Sub-Riemannian Isoperimetric Problem Tipo de documento: documento electrónico Autores: Capogna, Luca ; SpringerLink (Online service) ; Pauls, Scott D ; Danielli, Donatella ; Tyson, Jeremy T Editorial: Basel : Birkhäuser Basel Fecha de publicación: 2007 Colección: Progress in Mathematics num. 259 Número de páginas: XVI, 224 p Il.: online resource ISBN/ISSN/DL: 978-3-7643-8133-2 Idioma : Inglés (eng) Palabras clave: Mathematics Topological groups Lie Global analysis (Mathematics) Manifolds Partial differential equations System theory Differential geometry Complex manifolds Geometry Groups, Groups and Cell Complexes (incl. Diff.Topology) Equations Analysis on Systems Theory, Control Clasificación: 51 Matemáticas Resumen: The past decade has witnessed a dramatic and widespread expansion of interest and activity in sub-Riemannian (Carnot-Caratheodory) geometry, motivated both internally by its role as a basic model in the modern theory of analysis on metric spaces, and externally through the continuous development of applications (both classical and emerging) in areas such as control theory, robotic path planning, neurobiology and digital image reconstruction. The quintessential example of a sub Riemannian structure is the Heisenberg group, which is a nexus for all of the aforementioned applications as well as a point of contact between CR geometry, Gromov hyperbolic geometry of complex hyperbolic space, subelliptic PDE, jet spaces, and quantum mechanics. This book provides an introduction to the basics of sub-Riemannian differential geometry and geometric analysis in the Heisenberg group, focusing primarily on the current state of knowledge regarding Pierre Pansu's celebrated 1982 conjecture regarding the sub-Riemannian isoperimetric profile. It presents a detailed description of Heisenberg submanifold geometry and geometric measure theory, which provides an opportunity to collect for the first time in one location the various known partial results and methods of attack on Pansu's problem. As such it serves simultaneously as an introduction to the area for graduate students and beginning researchers, and as a research monograph focused on the isoperimetric problem suitable for experts in the area Nota de contenido: The Isoperimetric Problem in Euclidean Space -- The Heisenberg Group and Sub-Riemannian Geometry -- Applications of Heisenberg Geometry -- Horizontal Geometry of Submanifolds -- Sobolev and BV Spaces -- Geometric Measure Theory and Geometric Function Theory -- The Isoperimetric Inequality in ? -- The Isoperimetric Profile of ? -- Best Constants for Other Geometric Inequalities on the Heisenberg Group En línea: http://dx.doi.org/10.1007/978-3-7643-8133-2 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34700 An Introduction to the Heisenberg Group and the Sub-Riemannian Isoperimetric Problem [documento electrónico] / Capogna, Luca ; SpringerLink (Online service) ; Pauls, Scott D ; Danielli, Donatella ; Tyson, Jeremy T . - Basel : Birkhäuser Basel, 2007 . - XVI, 224 p : online resource. - (Progress in Mathematics; 259) .
ISBN : 978-3-7643-8133-2
Idioma : Inglés (eng)
Palabras clave: Mathematics Topological groups Lie Global analysis (Mathematics) Manifolds Partial differential equations System theory Differential geometry Complex manifolds Geometry Groups, Groups and Cell Complexes (incl. Diff.Topology) Equations Analysis on Systems Theory, Control Clasificación: 51 Matemáticas Resumen: The past decade has witnessed a dramatic and widespread expansion of interest and activity in sub-Riemannian (Carnot-Caratheodory) geometry, motivated both internally by its role as a basic model in the modern theory of analysis on metric spaces, and externally through the continuous development of applications (both classical and emerging) in areas such as control theory, robotic path planning, neurobiology and digital image reconstruction. The quintessential example of a sub Riemannian structure is the Heisenberg group, which is a nexus for all of the aforementioned applications as well as a point of contact between CR geometry, Gromov hyperbolic geometry of complex hyperbolic space, subelliptic PDE, jet spaces, and quantum mechanics. This book provides an introduction to the basics of sub-Riemannian differential geometry and geometric analysis in the Heisenberg group, focusing primarily on the current state of knowledge regarding Pierre Pansu's celebrated 1982 conjecture regarding the sub-Riemannian isoperimetric profile. It presents a detailed description of Heisenberg submanifold geometry and geometric measure theory, which provides an opportunity to collect for the first time in one location the various known partial results and methods of attack on Pansu's problem. As such it serves simultaneously as an introduction to the area for graduate students and beginning researchers, and as a research monograph focused on the isoperimetric problem suitable for experts in the area Nota de contenido: The Isoperimetric Problem in Euclidean Space -- The Heisenberg Group and Sub-Riemannian Geometry -- Applications of Heisenberg Geometry -- Horizontal Geometry of Submanifolds -- Sobolev and BV Spaces -- Geometric Measure Theory and Geometric Function Theory -- The Isoperimetric Inequality in ? -- The Isoperimetric Profile of ? -- Best Constants for Other Geometric Inequalities on the Heisenberg Group En línea: http://dx.doi.org/10.1007/978-3-7643-8133-2 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34700 Ejemplares
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Título : Arithmetic and Geometry Around Hypergeometric Functions : Lecture Notes of a CIMPA Summer School held at Galatasaray University, Istanbul, 2005 Tipo de documento: documento electrónico Autores: SpringerLink (Online service) ; Holzapfel, Rolf-Peter ; Uludag, A. Muhammed ; Yoshida, Masaaki Editorial: Basel : Birkhäuser Basel Fecha de publicación: 2007 Colección: Progress in Mathematics num. 260 Número de páginas: VIII, 437 p Il.: online resource ISBN/ISSN/DL: 978-3-7643-8284-1 Idioma : Inglés (eng) Palabras clave: Mathematics Algebraic geometry Special functions Functions Geometry Clasificación: 51 Matemáticas Resumen: This volume comprises the Lecture Notes of the CIMPA Summer School "Arithmetic and Geometry around Hypergeometric Functions" held at Galatasaray University, Istanbul in 2005. It contains lecture notes, a survey article, research articles, and the results of a problem session. Key topics are moduli spaces of points on P1 and Picard-Terada-Deligne-Mostow theory, moduli spaces of K3 surfaces, complex hyperbolic geometry, ball quotients, GKZ hypergeometric structures, Hilbert and Picard modular surfaces, uniformizations of complex orbifolds, algebraicity of values of Schwartz triangle functions, and Thakur's hypergeometric function. The book provides a background, gives detailed expositions and indicates new research directions. It is directed to postgraduate students and researchers Nota de contenido: Hyperbolic Geometry and the Moduli Space of Real Binary Sextics -- Gauss’ Hypergeometric Function -- Moduli of K3 Surfaces and Complex Ball Quotients -- Macbeaths infinite series of Hurwitz groups -- Relative Proportionality on Picard and Hilbert Modular Surfaces -- Hypergeometric Functions and Carlitz Differential Equations over Function Fields -- The Moduli Space of 5 Points on ?1 and K3 Surfaces -- Uniformization by Lauricella Functions — An Overview of the Theory of Deligne-Mostow -- Invariant Functions with Respect to the Whitehead-Link -- On the Construction of Class Fields by Picard Modular Forms -- Algebraic Values of Schwarz Triangle Functions -- GKZ Hypergeometric Structures -- Orbifolds and Their Uniformization -- From the Power Function to the Hypergeometric Function -- Problem Session En línea: http://dx.doi.org/10.1007/978-3-7643-8284-1 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34707 Arithmetic and Geometry Around Hypergeometric Functions : Lecture Notes of a CIMPA Summer School held at Galatasaray University, Istanbul, 2005 [documento electrónico] / SpringerLink (Online service) ; Holzapfel, Rolf-Peter ; Uludag, A. Muhammed ; Yoshida, Masaaki . - Basel : Birkhäuser Basel, 2007 . - VIII, 437 p : online resource. - (Progress in Mathematics; 260) .
ISBN : 978-3-7643-8284-1
Idioma : Inglés (eng)
Palabras clave: Mathematics Algebraic geometry Special functions Functions Geometry Clasificación: 51 Matemáticas Resumen: This volume comprises the Lecture Notes of the CIMPA Summer School "Arithmetic and Geometry around Hypergeometric Functions" held at Galatasaray University, Istanbul in 2005. It contains lecture notes, a survey article, research articles, and the results of a problem session. Key topics are moduli spaces of points on P1 and Picard-Terada-Deligne-Mostow theory, moduli spaces of K3 surfaces, complex hyperbolic geometry, ball quotients, GKZ hypergeometric structures, Hilbert and Picard modular surfaces, uniformizations of complex orbifolds, algebraicity of values of Schwartz triangle functions, and Thakur's hypergeometric function. The book provides a background, gives detailed expositions and indicates new research directions. It is directed to postgraduate students and researchers Nota de contenido: Hyperbolic Geometry and the Moduli Space of Real Binary Sextics -- Gauss’ Hypergeometric Function -- Moduli of K3 Surfaces and Complex Ball Quotients -- Macbeaths infinite series of Hurwitz groups -- Relative Proportionality on Picard and Hilbert Modular Surfaces -- Hypergeometric Functions and Carlitz Differential Equations over Function Fields -- The Moduli Space of 5 Points on ?1 and K3 Surfaces -- Uniformization by Lauricella Functions — An Overview of the Theory of Deligne-Mostow -- Invariant Functions with Respect to the Whitehead-Link -- On the Construction of Class Fields by Picard Modular Forms -- Algebraic Values of Schwarz Triangle Functions -- GKZ Hypergeometric Structures -- Orbifolds and Their Uniformization -- From the Power Function to the Hypergeometric Function -- Problem Session En línea: http://dx.doi.org/10.1007/978-3-7643-8284-1 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34707 Ejemplares
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Título : Arrangements, Local Systems and Singularities : CIMPA Summer School, Galatasaray University, Istanbul, 2007 Tipo de documento: documento electrónico Autores: SpringerLink (Online service) ; Zein, Fouad El ; Suciu, Alexandru I ; Tosun, Meral ; Uludag, A. Muhammed ; Yuzvinsky, Sergey Editorial: Basel : Birkhäuser Basel Fecha de publicación: 2010 Colección: Progress in Mathematics num. 283 Número de páginas: 305 p Il.: online resource ISBN/ISSN/DL: 978-3-0346-0209-9 Idioma : Inglés (eng) Palabras clave: Mathematics Algebraic geometry Geometry Clasificación: 51 Matemáticas Nota de contenido: Combinatorics of Covers of Complexified Hyperplane Arrangements -- Homological Aspects of Hyperplane Arrangements -- Pencils of Plane Curves and Characteristic Varieties -- Lectures on Orlik-Solomon Algebras -- Local Systems and Constructible Sheaves -- Geometry and Combinatorics of Resonant Weights -- The Characteristic Quasi-Polynomials of the Arrangements of Root Systems and Mid-Hyperplane Arrangements -- Toric Varieties and the Diagonal Property -- to Plane Curve Singularities. Toric Resolution Tower and Puiseux Pairs -- Surface Singularities Appeared in the Hyperbolic Schwarz Map for the Hypergeometric Equation -- On the Extendability of Free Multiarrangements -- Problem Session En línea: http://dx.doi.org/10.1007/978-3-0346-0209-9 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33668 Arrangements, Local Systems and Singularities : CIMPA Summer School, Galatasaray University, Istanbul, 2007 [documento electrónico] / SpringerLink (Online service) ; Zein, Fouad El ; Suciu, Alexandru I ; Tosun, Meral ; Uludag, A. Muhammed ; Yuzvinsky, Sergey . - Basel : Birkhäuser Basel, 2010 . - 305 p : online resource. - (Progress in Mathematics; 283) .
ISBN : 978-3-0346-0209-9
Idioma : Inglés (eng)
Palabras clave: Mathematics Algebraic geometry Geometry Clasificación: 51 Matemáticas Nota de contenido: Combinatorics of Covers of Complexified Hyperplane Arrangements -- Homological Aspects of Hyperplane Arrangements -- Pencils of Plane Curves and Characteristic Varieties -- Lectures on Orlik-Solomon Algebras -- Local Systems and Constructible Sheaves -- Geometry and Combinatorics of Resonant Weights -- The Characteristic Quasi-Polynomials of the Arrangements of Root Systems and Mid-Hyperplane Arrangements -- Toric Varieties and the Diagonal Property -- to Plane Curve Singularities. Toric Resolution Tower and Puiseux Pairs -- Surface Singularities Appeared in the Hyperbolic Schwarz Map for the Hypergeometric Equation -- On the Extendability of Free Multiarrangements -- Problem Session En línea: http://dx.doi.org/10.1007/978-3-0346-0209-9 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33668 Ejemplares
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Título : Determinantal Ideals Tipo de documento: documento electrónico Autores: Miró-Roig, Rosa M ; SpringerLink (Online service) Editorial: Basel : Birkhäuser Basel Fecha de publicación: 2008 Colección: Progress in Mathematics num. 264 Número de páginas: XVI, 140 p Il.: online resource ISBN/ISSN/DL: 978-3-7643-8535-4 Idioma : Inglés (eng) Palabras clave: Mathematics Commutative algebra rings Combinatorics Rings and Algebras Clasificación: 51 Matemáticas Resumen: Determinantal ideals are ideals generated by minors of a homogeneous polynomial matrix. Some classical ideals that can be generated in this way are the ideal of the Veronese varieties, of the Segre varieties, and of the rational normal scrolls. Determinantal ideals are a central topic in both commutative algebra and algebraic geometry, and they also have numerous connections with invariant theory, representation theory, and combinatorics. Due to their important role, their study has attracted many researchers and has received considerable attention in the literature. In this book three crucial problems are addressed: CI-liaison class and G-liaison class of standard determinantal ideals; the multiplicity conjecture for standard determinantal ideals; and unobstructedness and dimension of families of standard determinantal ideals Nota de contenido: Background -- CI-liaison and G-liaison of Standard Determinantal Ideals -- Multiplicity Conjecture for Standard Determinantal Ideals -- Unobstructedness and Dimension of Families of Standard Determinantal Ideals -- Determinantal Ideals, Symmetric Determinantal Ideals, and Open Problems En línea: http://dx.doi.org/10.1007/978-3-7643-8535-4 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34392 Determinantal Ideals [documento electrónico] / Miró-Roig, Rosa M ; SpringerLink (Online service) . - Basel : Birkhäuser Basel, 2008 . - XVI, 140 p : online resource. - (Progress in Mathematics; 264) .
ISBN : 978-3-7643-8535-4
Idioma : Inglés (eng)
Palabras clave: Mathematics Commutative algebra rings Combinatorics Rings and Algebras Clasificación: 51 Matemáticas Resumen: Determinantal ideals are ideals generated by minors of a homogeneous polynomial matrix. Some classical ideals that can be generated in this way are the ideal of the Veronese varieties, of the Segre varieties, and of the rational normal scrolls. Determinantal ideals are a central topic in both commutative algebra and algebraic geometry, and they also have numerous connections with invariant theory, representation theory, and combinatorics. Due to their important role, their study has attracted many researchers and has received considerable attention in the literature. In this book three crucial problems are addressed: CI-liaison class and G-liaison class of standard determinantal ideals; the multiplicity conjecture for standard determinantal ideals; and unobstructedness and dimension of families of standard determinantal ideals Nota de contenido: Background -- CI-liaison and G-liaison of Standard Determinantal Ideals -- Multiplicity Conjecture for Standard Determinantal Ideals -- Unobstructedness and Dimension of Families of Standard Determinantal Ideals -- Determinantal Ideals, Symmetric Determinantal Ideals, and Open Problems En línea: http://dx.doi.org/10.1007/978-3-7643-8535-4 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34392 Ejemplares
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Título : Dimension and Recurrence in Hyperbolic Dynamics Tipo de documento: documento electrónico Autores: Luis Barreira ; SpringerLink (Online service) Editorial: Basel : Birkhäuser Basel Fecha de publicación: 2008 Colección: Progress in Mathematics num. 272 Número de páginas: XIV, 300 p Il.: online resource ISBN/ISSN/DL: 978-3-7643-8882-9 Idioma : Inglés (eng) Palabras clave: Mathematics Mathematical analysis Analysis (Mathematics) Dynamics Ergodic theory Manifolds Complex manifolds Dynamical Systems and Theory Cell Complexes (incl. Diff.Topology) Clasificación: 51 Matemáticas Resumen: The main objective of this book is to give a broad unified introduction to the study of dimension and recurrence in hyperbolic dynamics. It includes the discussion of the foundations, main results, and main techniques in the rich interplay of four main areas of research: hyperbolic dynamics, dimension theory, multifractal analysis, and quantitative recurrence. It also gives a panorama of several selected topics of current research interest. More than half of the material appears here for the first time in book form, describing many recent developments in the area such as topics on irregular sets, variational principles, applications to number theory, measures of maximal dimension, multifractal nonrigidity, and quantitative recurrence. All the results are included with detailed proofs, many of them simplified or rewritten on purpose for the book. The text is self-contained and directed to researchers as well as graduate students that wish to have a global view of the theory together with a working knowledge of its main techniques. It will also be useful as as basis for graduate courses in dimension theory of dynamical systems, multifractal analysis, and pointwise dimension and recurrence in hyperbolic dynamics Nota de contenido: Basic Notions -- Basic Notions -- Dimension Theory -- Dimension Theory and Thermodynamic Formalism -- Repellers and Hyperbolic Sets -- Measures of Maximal Dimension -- Multifractal Analysis: Core Theory -- Multifractal Analysis of Equilibrium Measures -- General Concept of Multifractal Analysis -- Dimension of Irregular Sets -- Variational Principles in Multifractal Analysis -- Multifractal Analysis: Further Developments -- Multidimensional Spectra and Number Theory -- Multifractal Rigidity -- Hyperbolic Sets: Past and Future -- Hyperbolicity and Recurrence -- Pointwise Dimension for Hyperbolic Dynamics -- Product Structure of Hyperbolic Measures -- Quantitative Recurrence and Dimension Theory En línea: http://dx.doi.org/10.1007/978-3-7643-8882-9 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34424 Dimension and Recurrence in Hyperbolic Dynamics [documento electrónico] / Luis Barreira ; SpringerLink (Online service) . - Basel : Birkhäuser Basel, 2008 . - XIV, 300 p : online resource. - (Progress in Mathematics; 272) .
ISBN : 978-3-7643-8882-9
Idioma : Inglés (eng)
Palabras clave: Mathematics Mathematical analysis Analysis (Mathematics) Dynamics Ergodic theory Manifolds Complex manifolds Dynamical Systems and Theory Cell Complexes (incl. Diff.Topology) Clasificación: 51 Matemáticas Resumen: The main objective of this book is to give a broad unified introduction to the study of dimension and recurrence in hyperbolic dynamics. It includes the discussion of the foundations, main results, and main techniques in the rich interplay of four main areas of research: hyperbolic dynamics, dimension theory, multifractal analysis, and quantitative recurrence. It also gives a panorama of several selected topics of current research interest. More than half of the material appears here for the first time in book form, describing many recent developments in the area such as topics on irregular sets, variational principles, applications to number theory, measures of maximal dimension, multifractal nonrigidity, and quantitative recurrence. All the results are included with detailed proofs, many of them simplified or rewritten on purpose for the book. The text is self-contained and directed to researchers as well as graduate students that wish to have a global view of the theory together with a working knowledge of its main techniques. It will also be useful as as basis for graduate courses in dimension theory of dynamical systems, multifractal analysis, and pointwise dimension and recurrence in hyperbolic dynamics Nota de contenido: Basic Notions -- Basic Notions -- Dimension Theory -- Dimension Theory and Thermodynamic Formalism -- Repellers and Hyperbolic Sets -- Measures of Maximal Dimension -- Multifractal Analysis: Core Theory -- Multifractal Analysis of Equilibrium Measures -- General Concept of Multifractal Analysis -- Dimension of Irregular Sets -- Variational Principles in Multifractal Analysis -- Multifractal Analysis: Further Developments -- Multidimensional Spectra and Number Theory -- Multifractal Rigidity -- Hyperbolic Sets: Past and Future -- Hyperbolicity and Recurrence -- Pointwise Dimension for Hyperbolic Dynamics -- Product Structure of Hyperbolic Measures -- Quantitative Recurrence and Dimension Theory En línea: http://dx.doi.org/10.1007/978-3-7643-8882-9 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34424 Ejemplares
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