Overview
- Comprehensive account of very recent results in geometric analysis
- Essentially self-contained, supplying the necessary background material which is not easily available in book form and presenting much of it in a new, original form
- Includes supplementary material: sn.pub/extras
Part of the book series: Progress in Mathematics (PM, volume 266)
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About this book
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.
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Table of contents (9 chapters)
Authors and Affiliations
Bibliographic Information
Book Title: Vanishing and Finiteness Results in Geometric Analysis
Book Subtitle: A Generalization of the Bochner Technique
Authors: Stefano Pigola, Alberto G. Setti, Marco Rigoli
Series Title: Progress in Mathematics
DOI: https://doi.org/10.1007/978-3-7643-8642-9
Publisher: Birkhäuser Basel
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Birkhäuser Basel 2008
Hardcover ISBN: 978-3-7643-8641-2Published: 17 April 2008
eBook ISBN: 978-3-7643-8642-9Published: 28 May 2008
Series ISSN: 0743-1643
Series E-ISSN: 2296-505X
Edition Number: 1
Number of Pages: XIV, 282
Topics: Differential Geometry, Global Analysis and Analysis on Manifolds, Analysis