Frontiers in Mathematics

Geometric Analysis of Quasilinear Inequalities on Complete Manifolds

Maximum and Compact Support Principles and Detours on Manifolds

Authors: Bianchini, B., Mari, L., Pucci, P., Rigoli, M.

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  • Investigates the validity of strong maximum principles, compact support principles and Liouville type theorems
  • Aims to give a unified view of recent results in the literature
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eBook 46,00 €
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  • ISBN 978-3-030-62704-1
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Softcover 57,19 €
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  • ISBN 978-3-030-62703-4
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About this book

This book demonstrates the influence of geometry on the qualitative behaviour of solutions of quasilinear PDEs on Riemannian manifolds. Motivated by examples arising, among others, from the theory of submanifolds, the authors study classes of coercive elliptic differential inequalities on domains of a manifold M with very general nonlinearities depending on the variable x, on the solution u and on its gradient. The book highlights the mean curvature operator and its variants, and investigates the validity of strong maximum principles, compact support principles and Liouville type theorems. In particular, it identifies sharp thresholds involving curvatures or volume growth of geodesic balls in M to guarantee the above properties under appropriate Keller-Osserman type conditions, which are investigated in detail throughout the book, and discusses the geometric reasons behind the existence of such thresholds. Further, the book also provides a unified review of recent results in the literature, and creates a bridge with geometry by studying the validity of weak and strong maximum principles at infinity, in the spirit of Omori-Yau’s Hessian and Laplacian principles and subsequent improvements.

Table of contents (10 chapters)

Table of contents (10 chapters)

Buy this book

eBook 46,00 €
price for Spain (gross)
  • ISBN 978-3-030-62704-1
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover 57,19 €
price for Spain (gross)
  • ISBN 978-3-030-62703-4
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Geometric Analysis of Quasilinear Inequalities on Complete Manifolds
Book Subtitle
Maximum and Compact Support Principles and Detours on Manifolds
Authors
Series Title
Frontiers in Mathematics
Copyright
2021
Publisher
Birkhäuser Basel
Copyright Holder
The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG
eBook ISBN
978-3-030-62704-1
DOI
10.1007/978-3-030-62704-1
Softcover ISBN
978-3-030-62703-4
Series ISSN
1660-8046
Edition Number
1
Number of Pages
X, 286
Number of Illustrations
1 b/w illustrations
Topics