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Maximum Principles and Geometric Applications

  • Luis J. Alías
  • Paolo Mastrolia
  • Marco Rigoli
Book

Part of the Springer Monographs in Mathematics book series (SMM)

Table of contents

  1. Front Matter
    Pages i-xxvii
  2. Luis J. Alías, Paolo Mastrolia, Marco Rigoli
    Pages 1-76
  3. Luis J. Alías, Paolo Mastrolia, Marco Rigoli
    Pages 77-139
  4. Luis J. Alías, Paolo Mastrolia, Marco Rigoli
    Pages 141-201
  5. Luis J. Alías, Paolo Mastrolia, Marco Rigoli
    Pages 203-270
  6. Luis J. Alías, Paolo Mastrolia, Marco Rigoli
    Pages 271-324
  7. Luis J. Alías, Paolo Mastrolia, Marco Rigoli
    Pages 325-383
  8. Luis J. Alías, Paolo Mastrolia, Marco Rigoli
    Pages 385-441
  9. Luis J. Alías, Paolo Mastrolia, Marco Rigoli
    Pages 443-498
  10. Luis J. Alías, Paolo Mastrolia, Marco Rigoli
    Pages 499-552
  11. Back Matter
    Pages 553-570

About this book

Introduction

This monograph presents an introduction to some geometric and analytic aspects of the maximum principle. In doing so, it analyses with great detail the mathematical tools and geometric foundations needed to develop the various new forms that are presented in the first chapters of the book. In particular, a generalization of the Omori-Yau maximum principle to a wide class of differential operators is given, as well as a corresponding weak maximum principle and its equivalent open form and parabolicity as a special stronger formulation of the latter. 

In the second part, the attention focuses on a wide range of applications, mainly to geometric problems, but also on some analytic (especially PDEs) questions including: the geometry of submanifolds, hypersurfaces in Riemannian and Lorentzian targets, Ricci solitons, Liouville theorems, uniqueness of solutions of Lichnerowicz-type PDEs and so on.

Maximum Principles and Geometric Applications is written in an easy style making it accessible to beginners. The reader is guided with a detailed presentation of some topics of Riemannian geometry that are usually not covered in textbooks. Furthermore, many of the results and even proofs of known results are new and lead to the frontiers of a contemporary and active field of research.

Keywords

Maximum Principles Elliptic Differential Operators Parabolicity Stochastic Completeness Liouville Type Results Isometric Immersions Constant Curvature Hypersurfaces Newton Operators Ricci Solitons Space-like Hypersurfaces

Authors and affiliations

  • Luis J. Alías
    • 1
  • Paolo Mastrolia
    • 2
  • Marco Rigoli
    • 3
  1. 1.Departamento de MatemáticasUniversidad de MurciaMurciaSpain
  2. 2.Dipartimento di MatematicaUniversità degli Studi di MilanoMilanItaly
  3. 3.Dipartimento di MatematicaUniversità degli Studi di MilanoMilanItaly

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-24337-5
  • Copyright Information Springer International Publishing Switzerland 2016
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-24335-1
  • Online ISBN 978-3-319-24337-5
  • Series Print ISSN 1439-7382
  • Series Online ISSN 2196-9922
  • Buy this book on publisher's site
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