Frontiers in Mathematics

Geometric Analysis of Quasilinear Inequalities on Complete Manifolds

Maximum and Compact Support Principles and Detours on Manifolds

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

Vorschau
  • 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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  • ISBN 978-3-030-62704-1
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Über dieses Buch

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.

Inhaltsverzeichnis (10 Kapitel)

Inhaltsverzeichnis (10 Kapitel)

Dieses Buch kaufen

eBook 46,00 €
Preis für Deutschland (Brutto)
  • ISBN 978-3-030-62704-1
  • Versehen mit digitalem Wasserzeichen, DRM-frei
  • Erhältliche Formate: PDF, EPUB
  • eBooks sind auf allen Endgeräten nutzbar
  • Sofortiger eBook Download nach Kauf
Softcover 58,84 €
Preis für Deutschland (Brutto)
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Bibliografische Information

Bibliographic Information
Buchtitel
Geometric Analysis of Quasilinear Inequalities on Complete Manifolds
Buchuntertitel
Maximum and Compact Support Principles and Detours on Manifolds
Autoren
Titel der Buchreihe
Frontiers in Mathematics
Copyright
2021
Verlag
Birkhäuser Basel
Copyright Inhaber
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
Buchreihen ISSN
1660-8046
Auflage
1
Seitenzahl
X, 286
Anzahl der Bilder
1 schwarz-weiß Abbildungen
Themen