Vanishing and finiteness results in geometric analysis
Subtitle: a generalization of the Bochner technique
By: Stefano Pigola, Marco Rigoli, Alberto G. Setti.
Contributors: Rigoli, Marco.; Setti, Alberto G. 1960-
Series: Progress in mathematics -- v. 266; Progress in mathematics (Boston, Mass.) -- v. 266.
Publisher: Birkhauser
Published: 2008
Place of publication: Basel; Boston
Language: eng
Number of pages: 282
ISBN-13: 9783764386412
Subjects: Riemannian manifolds; Bochner technique; Geometry, Riemannian; Differential equations
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, L[superscript p] cohomology, metric rigidity of manifolds with positive spectrum, and structure theorems for Kahler manifolds."--Jacket.
Notes: Includes bibliographical references (p. [269]-279) and index.