ENGLISH

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

By Stefano Pigola , Alberto G. Setti , Marco Rigoli (auth.)

Book information

Publisher
Birkhäuser Basel
Year
2008
ISBN
376438641X, 9783764386412, 9783764386429
DOI
10.1007/978-3-7643-8642-9
Open Library ID
OL17006951M
Language
english
Format
PDF
Filesize
1 MB (1569278 bytes)
Series
Progress in Mathematics 266
Edition
1
Pages
282\294
Library
Kolxo3
Scanned
yes
Time added
2009-07-20 03:45:11
Differential Geometry; Global Analysis and Analysi

Description

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.

Similar books