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Vanishing and Finiteness Results in Geometric Analysis: A Generalization of the Bochner Technique
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Catalogue Information
Field name
Details
Dewey Class
516.36
Title
Vanishing and Finiteness Results in Geometric Analysis ([EBook]) : A Generalization of the Bochner Technique / by Stefano Pigola, Alberto G. Setti, Marco Rigoli.
Author
Pigola, Stefano. , 1973-
Added Personal Name
Setti, Alberto G.
Rigoli, Marco
Other name(s)
SpringerLink (Online service)
Publication
Basel : Birkhäuser , 2008.
Physical Details
: online resource.
Series
Progress in mathematics
; 266
ISBN
9783764386429
Summary Note
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, Lp 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.:
Contents note
Introduction -- 1. Harmonic, pluriharmonic, holomorphic maps and basic Hermitian and Kählerian geometry -- 2. Comparison Results -- 3. Review of spectral theory -- 4. Vanishing results -- 5. A finite-dimensionality result -- 6. Applications to harmonic maps -- 7. Some topological applications -- 8. Constancy of holomorphic maps and the structure of complete Kahler manifolds -- 9. Splitting and gap theorems in the presence of a Poincaré-Sobolev inequality -- Appendices -- Bibliography -- Index.
System details note
Online resource is restricted to subscription institutions through IP address (only for SISSA users)
Internet Site
http://dx.doi.org/10.1007/978-3-7643-8642-9
Links to Related Works
Subject References:
Analysis
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Differential Geometry
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Geometry, Differential
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Global analysis
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Global Analysis and Analysis on Manifolds
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Global analysis (Mathematics)
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Global differential geometry
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Riemannian manifolds
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Authors:
author
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Pigola, Stefano. 1973-
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Rigoli, Marco
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Setti, Alberto G.
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Corporate Authors:
SpringerLink (Online service)
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Series:
Progress in mathematics
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Classification:
516.36
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516.36 (DDC 23)
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