Progress in Mathematics

Yamabe-type Equations on Complete, Noncompact Manifolds

Authors: Mastrolia, Paolo, Rigoli, Marco, Setti, Alberto G

  • Up-to-date results on the subject not yet available in book form
  • A number of new results and techniques as well as new proofs of known results
  • Clear account of a number of key methods from geometric analysis accessible to non-specialists in the field
  • Self-contained treatment, detailed description of both the geometric and the main analytic tools exploited
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  • ISBN 978-3-0348-0791-3
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About this book

The aim of this monograph is to present a self-contained introduction to some geometric and analytic aspects of the Yamabe problem. The book also describes a wide range of methods and techniques that can be successfully applied to nonlinear differential equations in particularly challenging situations. Such situations occur where the lack of compactness, symmetry and homogeneity prevents the use of more standard tools typically used in compact situations or for the Euclidean setting. The work is written in an easy style that makes it accessible even to non-specialists.

After a self-contained treatment of the geometric tools used in the book, readers are introduced to the main subject by means of a concise but clear study of some aspects of the Yamabe problem on compact manifolds. This study provides the motivation and geometrical feeling for the subsequent part of the work. In the main body of the book, it is shown how the geometry and the analysis of nonlinear partial differential equations blend together to give up-to-date results on existence, nonexistence, uniqueness and a priori estimates for solutions of general Yamabe-type equations and inequalities on complete, non-compact Riemannian manifolds.

Reviews

From the reviews:

“This monograph concerns solving nonlinear partial differential equations on manifolds, specifically equations of Yamabe type. … This monograph provides a good introduction to current research on nonlinear partial differential equations on noncompact manifolds for graduate students and researchers.” (David L. Finn, Mathematical Reviews, October, 2013)

Table of contents (7 chapters)

Buy this book

eBook $99.00
price for USA (gross)
  • ISBN 978-3-0348-0376-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $129.00
price for USA
  • ISBN 978-3-0348-0375-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $129.00
price for USA
  • ISBN 978-3-0348-0791-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Yamabe-type Equations on Complete, Noncompact Manifolds
Authors
Series Title
Progress in Mathematics
Series Volume
302
Copyright
2012
Publisher
Birkhäuser Basel
Copyright Holder
Springer Basel
eBook ISBN
978-3-0348-0376-2
DOI
10.1007/978-3-0348-0376-2
Hardcover ISBN
978-3-0348-0375-5
Softcover ISBN
978-3-0348-0791-3
Series ISSN
0743-1643
Edition Number
1
Number of Pages
VIII, 260
Topics