Progress in Mathematics

Vanishing and Finiteness Results in Geometric Analysis

A Generalization of the Bochner Technique

Authors: Pigola, Stefano, Rigoli, Marco, Setti, Alberto G

  • Offers a comprehensive account of very recent results in geometric analysis
  • Essentially self-contained, supplies the necessary background material which is not easily available in book form and presents much of it in a new, original form
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Hardcover $109.00
price for USA in USD
  • ISBN 978-3-7643-8641-2
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About this book

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.

Table of contents (9 chapters)

Buy this book

eBook $84.99
price for USA in USD (gross)
  • ISBN 978-3-7643-8642-9
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $109.00
price for USA in USD
  • ISBN 978-3-7643-8641-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Vanishing and Finiteness Results in Geometric Analysis
Book Subtitle
A Generalization of the Bochner Technique
Authors
Series Title
Progress in Mathematics
Series Volume
266
Copyright
2008
Publisher
Birkhäuser Basel
Copyright Holder
Birkhäuser Basel
eBook ISBN
978-3-7643-8642-9
DOI
10.1007/978-3-7643-8642-9
Hardcover ISBN
978-3-7643-8641-2
Series ISSN
0743-1643
Edition Number
1
Number of Pages
XIV, 282
Topics