Vanishing and Finiteness Results in Geometric Analysis / Pigola, Stefano (2008)  

Público ISBD Título : Vanishing and Finiteness Results in Geometric Analysis : A Generalization of the Bochner Technique Tipo de documento: documento electrónico Autores: Pigola, Stefano ; SpringerLink (Online service) ; Setti, Alberto G ; Rigoli, Marco Editorial: Basel : Birkhäuser Basel Fecha de publicación: 2008 Colección: Progress in Mathematics num. 266 Número de páginas: XIV, 282 p Il.: online resource ISBN/ISSN/DL: 978-3-7643-8642-9 Idioma : Inglés (eng) Palabras clave: Mathematics  Mathematical  analysis  Analysis  (Mathematics)  Global  Manifolds  Differential  geometry  Geometry  and  on Clasificación: 51 Matemáticas Resumen: This book presents very recent results involving an extensive use of analytical tools in the study of geometrical and topological properties of complete Riemannian manifolds. It analyzes in detail an extension of the Bochner technique to the non compact setting, yielding conditions which ensure that solutions of geometrically significant differential equations either are trivial (vanishing results) or give rise to finite dimensional vector spaces (finiteness results). The book develops a range of methods from spectral theory and qualitative properties of solutions of PDEs to comparison theorems in Riemannian geometry and potential theory. All needed tools are described in detail, often with an original approach. Some of the applications presented concern the topology at infinity of submanifolds, Lp cohomology, metric rigidity of manifolds with positive spectrum, and structure theorems for Kähler manifolds. The book is essentially self-contained and supplies in an original presentation the necessary background material not easily available in book form Nota de contenido: Harmonic, pluriharmonic, holomorphic maps and basic Hermitian and Kählerian geometry -- Comparison Results -- Review of spectral theory -- Vanishing results -- A finite-dimensionality result -- Applications to harmonic maps -- Some topological applications -- Constancy of holomorphic maps and the structure of complete Kähler manifolds -- Splitting and gap theorems in the presence of a Poincaré-Sobolev inequality En línea: http://dx.doi.org/10.1007/978-3-7643-8642-9 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34403 Vanishing and Finiteness Results in Geometric Analysis : A Generalization of the Bochner Technique [documento electrónico] / Pigola, Stefano ; SpringerLink (Online service) ; Setti, Alberto G ; Rigoli, Marco . - Basel : Birkhäuser Basel, 2008 . - XIV, 282 p : online resource. - (Progress in Mathematics; 266) . ISBN : 978-3-7643-8642-9 Idioma : Inglés (eng) Palabras clave: Mathematics  Mathematical  analysis  Analysis  (Mathematics)  Global  Manifolds  Differential  geometry  Geometry  and  on Clasificación: 51 Matemáticas Resumen: This book presents very recent results involving an extensive use of analytical tools in the study of geometrical and topological properties of complete Riemannian manifolds. It analyzes in detail an extension of the Bochner technique to the non compact setting, yielding conditions which ensure that solutions of geometrically significant differential equations either are trivial (vanishing results) or give rise to finite dimensional vector spaces (finiteness results). The book develops a range of methods from spectral theory and qualitative properties of solutions of PDEs to comparison theorems in Riemannian geometry and potential theory. All needed tools are described in detail, often with an original approach. Some of the applications presented concern the topology at infinity of submanifolds, Lp cohomology, metric rigidity of manifolds with positive spectrum, and structure theorems for Kähler manifolds. The book is essentially self-contained and supplies in an original presentation the necessary background material not easily available in book form Nota de contenido: Harmonic, pluriharmonic, holomorphic maps and basic Hermitian and Kählerian geometry -- Comparison Results -- Review of spectral theory -- Vanishing results -- A finite-dimensionality result -- Applications to harmonic maps -- Some topological applications -- Constancy of holomorphic maps and the structure of complete Kähler manifolds -- Splitting and gap theorems in the presence of a Poincaré-Sobolev inequality En línea: http://dx.doi.org/10.1007/978-3-7643-8642-9 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34403

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Yamabe-type Equations on Complete, Noncompact Manifolds / Mastrolia, Paolo (2012)  

Público ISBD Título : Yamabe-type Equations on Complete, Noncompact Manifolds Tipo de documento: documento electrónico Autores: Mastrolia, Paolo ; SpringerLink (Online service) ; Rigoli, Marco ; Setti, Alberto G Editorial: Basel : Springer Basel Fecha de publicación: 2012 Otro editor: Imprint: Birkhäuser Colección: Progress in Mathematics, ISSN 0743-1643 num. 302 Número de páginas: VIII, 260 p Il.: online resource ISBN/ISSN/DL: 978-3-0348-0376-2 Idioma : Inglés (eng) Palabras clave: Mathematics  Global  analysis  (Mathematics)  Manifolds  Differential  geometry  Geometry  Analysis  and  on Clasificación: 51 Matemáticas Resumen: The aim of this monograph is to present a self-contained introduction to some geometric and analytic aspects of the Yamabe problem. The book also describes a wide range of methods and techniques that can be successfully applied to nonlinear differential equations in particularly challenging situations. Such situations occur where the lack of compactness, symmetry and homogeneity prevents the use of more standard tools typically used in compact situations or for the Euclidean setting. The work is written in an easy style that makes it accessible even to non-specialists. After a self-contained treatment of the geometric tools used in the book, readers are introduced to the main subject by means of a concise but clear study of some aspects of the Yamabe problem on compact manifolds. This study provides the motivation and geometrical feeling for the subsequent part of the work. In the main body of the book, it is shown how the geometry and the analysis of nonlinear partial differential equations blend together to give up-to-date results on existence, nonexistence, uniqueness and a priori estimates for solutions of general Yamabe-type equations and inequalities on complete, non-compact Riemannian manifolds Nota de contenido: Introduction -- 1 Some Riemannian Geometry -- 2 Pointwise conformal metrics -- 3 General nonexistence results -- 4 A priori estimates -- 5 Uniqueness -- 6 Existence -- 7 Some special cases -- References -- Index En línea: http://dx.doi.org/10.1007/978-3-0348-0376-2 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32882 Yamabe-type Equations on Complete, Noncompact Manifolds [documento electrónico] / Mastrolia, Paolo ; SpringerLink (Online service) ; Rigoli, Marco ; Setti, Alberto G . - Basel : Springer Basel : Imprint: Birkhäuser, 2012 . - VIII, 260 p : online resource. - (Progress in Mathematics, ISSN 0743-1643; 302) . ISBN : 978-3-0348-0376-2 Idioma : Inglés (eng) Palabras clave: Mathematics  Global  analysis  (Mathematics)  Manifolds  Differential  geometry  Geometry  Analysis  and  on Clasificación: 51 Matemáticas Resumen: The aim of this monograph is to present a self-contained introduction to some geometric and analytic aspects of the Yamabe problem. The book also describes a wide range of methods and techniques that can be successfully applied to nonlinear differential equations in particularly challenging situations. Such situations occur where the lack of compactness, symmetry and homogeneity prevents the use of more standard tools typically used in compact situations or for the Euclidean setting. The work is written in an easy style that makes it accessible even to non-specialists. After a self-contained treatment of the geometric tools used in the book, readers are introduced to the main subject by means of a concise but clear study of some aspects of the Yamabe problem on compact manifolds. This study provides the motivation and geometrical feeling for the subsequent part of the work. In the main body of the book, it is shown how the geometry and the analysis of nonlinear partial differential equations blend together to give up-to-date results on existence, nonexistence, uniqueness and a priori estimates for solutions of general Yamabe-type equations and inequalities on complete, non-compact Riemannian manifolds Nota de contenido: Introduction -- 1 Some Riemannian Geometry -- 2 Pointwise conformal metrics -- 3 General nonexistence results -- 4 A priori estimates -- 5 Uniqueness -- 6 Existence -- 7 Some special cases -- References -- Index En línea: http://dx.doi.org/10.1007/978-3-0348-0376-2 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32882

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