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Vanishing and Finiteness Results in Geometric Analysis : A Generalization of the Bochner Technique (Hardcover)

Author: Pigola, Stefano

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Product Overview

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.


Publisher Textstream
Mfg Part# 9783764386412
SKU 206604738
Format Hardcover
ISBN10 376438641X
Release Date 8/13/2012
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