Vanishing and Finiteness Results in Geometric Analysis

Stefano Pigola

ISBN 10: 376438641X / ISBN 13: 9783764386412

Published by Birkhäuser Basel, Springer Basel Apr 2008, 2008

About this Item

Neuware -This book describes 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.Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, 14197 Berlin 300 pp. Englisch.

Seller Inventory # 9783764386412

Bibliographic Details

• Title: Vanishing and Finiteness Results in Geometric Analysis
• Publisher: Birkhäuser Basel, Springer Basel Apr 2008
• Publication Date: 2008
• Language: English
• ISBN 10: 376438641X
• ISBN 13: 9783764386412
• Binding: Buch
• Condition: Neu
• Dimensions: 241W x 160H x 21D millimeters 241 millimeters width by 160 millimeters height by 21 millimeters depth
• Weight: 617 grams

About this title

Synopsis

This book describes 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). To make up for the lack of compactness, 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. In addition, it describes all needed tools 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.

From the Back Cover

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^p 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.