Overview

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.

Full Product Details

Author:   Stefano Pigola ,  Marco Rigoli ,  Alberto G Setti
Publisher:   Birkhauser Verlag AG
Imprint:   Birkhauser Verlag AG
Edition:   2008 ed.
Volume:   266
Dimensions:   Width: 15.50cm , Height: 1.70cm , Length: 23.50cm
Weight:   0.617kg
ISBN:  

9783764386412

ISBN 10:   376438641
Pages:   282
Publication Date:   17 April 2008
Audience:   College/higher education ,  Undergraduate ,  Postgraduate, Research & Scholarly
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

Harmonic, pluriharmonic, holomorphic maps and basic Hermitian and Kahlerian geometry.- Comparison Results.- Review of spectral theory.- Vanishing results.- A finite-dimensionality result.- Applications to harmonic maps.- Some topological applications.- Constancy of holomorphic maps and the structure of complete Kahler manifolds.- Splitting and gap theorems in the presence of a Poincare-Sobolev inequality.

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