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© 2012

Yamabe-type Equations on Complete, Noncompact Manifolds

Book

Part of the Progress in Mathematics book series (PM, volume 302)

Table of contents

  1. Front Matter
    Pages i-vii
  2. Paolo Mastrolia, Marco Rigoli, Alberto G. Setti
    Pages 7-36
  3. Paolo Mastrolia, Marco Rigoli, Alberto G. Setti
    Pages 37-72
  4. Paolo Mastrolia, Marco Rigoli, Alberto G. Setti
    Pages 73-103
  5. Paolo Mastrolia, Marco Rigoli, Alberto G. Setti
    Pages 105-125
  6. Paolo Mastrolia, Marco Rigoli, Alberto G. Setti
    Pages 127-155
  7. Paolo Mastrolia, Marco Rigoli, Alberto G. Setti
    Pages 157-195
  8. Paolo Mastrolia, Marco Rigoli, Alberto G. Setti
    Pages 197-238
  9. Back Matter
    Pages 239-256

About this book

Introduction

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.

Keywords

Riemannian geometry via moving frames Yamabe-type equations a priori estimates, uniqueness and existence conformal deformation of the metric

Authors and affiliations

  1. 1., Dipartimento di MatematicaUniversità degli Studi di MilanoMilanoItaly
  2. 2., Dipartimento di MatematicaUniversità degli Studi di MilanoMilanoItaly
  3. 3., Dipartimento di Fisica e MatematicaUniversità dell'InsubriaComoItaly

Bibliographic information

  • Book Title Yamabe-type Equations on Complete, Noncompact Manifolds
  • Authors Paolo Mastrolia
    Marco Rigoli
    Alberto G Setti
  • Series Title Progress in Mathematics
  • Series Abbreviated Title Progress in Mathematics(Birkhäuser)
  • DOI https://doi.org/10.1007/978-3-0348-0376-2
  • Copyright Information Springer Basel 2012
  • Publisher Name Birkhäuser, Basel
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Hardcover ISBN 978-3-0348-0375-5
  • Softcover ISBN 978-3-0348-0791-3
  • eBook ISBN 978-3-0348-0376-2
  • Series ISSN 0743-1643
  • Series E-ISSN 2296-505X
  • Edition Number 1
  • Number of Pages VIII, 260
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Differential Geometry
    Global Analysis and Analysis on Manifolds
  • Buy this book on publisher's site

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)