Pigola, Rigoli, Setti Vanishing And Finiteness Results In Geometric Analysis (Birkhauser, 2008)(ISBN 376438641X)(294s) MDdg pdf (376438641X)

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Science/Engineering Vanishing and Finiteness Results in Geometric Analysis: A Generalization of the Bochner Technique

Posted on 2010-03-16

Name:	Science/Engineering Vanishing and Finiteness Results in Geometric Analysis: A Generalization of the Bochner Technique
ASIN/ISBN:	376438641X
Language:	English
File size:	1.5 Mb
Publisher:	Birkhauser Basel
Publish Date:	2008
ISBN:	376438641X
File Type:	PDF
Pages:	282 pages
File Size:	1,5 Mb

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Stefano Pigola, Marco Rigoli, Alberto G. Setti «Vanishing and Finiteness Results in Geometric Analysis: A Generalization of the Bochner Technique»

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 Kahler 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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