Vanishing And Finiteness Results In Geometric Analysis, A Generalization Of The Bochner Technique
Language: English
Published by Birkhäuser, 2008
- Hardcover
- New
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- Title
- Vanishing And Finiteness Results In Geometric Analysis, A Generalization Of The Bochner Technique
- Author
- Pigola, Stefano; Rigoli, Marco; Setti, Alberto G
- Publisher
- Birkhäuser
- Publication year
- 2008
- Condition
- New
- Binding
- Hardcover
- Language
- English
- ISBN 10
- 376438641X
- ISBN 13
- 9783764386412
- Series
- Book 81 of 170: Progress in Mathematics
This book describes 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). To make up for the lack of compactness, 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. In addition, it describes all needed tools 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.
"Synopsis" may belong to another edition of this title.
From the Back Cover
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.
"About the title" may belong to another edition of this title.
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