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

• Main Authors: Pigola, Stefano (Author), Setti, Alberto G. (Author), Rigoli, Marco (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Basel : Birkhäuser Basel, 2008.
• Series: Progress in Mathematics ; 266
• Subjects: Mathematics.; Mathematical analysis.; Analysis (Mathematics).; Global analysis (Mathematics).; Manifolds (Mathematics).; Differential geometry.; Differential Geometry.; Global Analysis and Analysis on Manifolds.; Analysis.

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...

Table of Contents:

• Harmonic, pluriharmonic, holomorphic maps and basic Hermitian and Kählerian 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 Kähler manifolds
• Splitting and gap theorems in the presence of a Poincaré-Sobolev inequality.