| Vanishing and Finiteness Results in Geometric Analysis: A Generalization of the Bochner Technique 2008 Edition Contributor(s): Pigola, Stefano (Author), Rigoli, Marco (Author), Setti, Alberto G. (Author) |
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ISBN: 376438641X ISBN-13: 9783764386412 Publisher: Birkhauser OUR PRICE: $52.24 Product Type: Hardcover - Other Formats Published: April 2008 Annotation: The aim of the book is to describe very recent results involving an extensive use of analytical tools in the study of geometrical and topological properties of complete Riemannian manifolds. An extension of the Bochner technique to the non compact setting is analyzed in detail, 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, a range of methods, from spectral theory and qualitative properties of solutions of PDEs, to comparison theorems in Riemannian geometry and potential theory, are developed. 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 Kaelher manifolds. |
| Additional Information |
| BISAC Categories: - Mathematics | Geometry - Differential - Mathematics | Mathematical Analysis |
| Dewey: 516.362 |
| LCCN: 2007941340 |
| Series: Progress in Mathematics |
| Physical Information: 0.8" H x 6.2" W x 9.2" (1.40 lbs) 300 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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). 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. |