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

Pigola, Stefano; Rigoli, Marco; Setti, Alberto G

Couverture rigide

ISBN 10 : 376438641X ISBN 13 : 9783764386412

Editeur : Birkhauser Verlag AG, 2008

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.

Détails de l'édition

• Éditeur: Birkhauser Verlag AG
• Date d'édition: 2008
• Langue: anglais
• ISBN 10: 376438641X
• ISBN 13: 9783764386412
• Reliure: Relié
• Nombre de pages: 296
• Coordonnées du fabricant: ProductSafety@springernature.com; ProductSafety@springernature.com; ; Poststr. 9; Darmstadt; 64293; Allemagne