Geometric Analysis of Quasilinear Inequalities on Complete Manifolds 1

Vetenskap & teknik

Geometric Analysis of Quasilinear Inequalities on Complete Manifolds

Bruno Bianchini • Luciano Mari • Patrizia Pucci • Marco Rigoli

Pocket

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286 sidor
2021

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-Yaus Hessian and Laplacian principles and subsequent improvements.

Författare: Bruno Bianchini, Luciano Mari, Patrizia Pucci, Marco Rigoli
Format: Pocket/Paperback
ISBN: 9783030627034
Språk: Engelska
Antal sidor: 286
Utgivningsdatum: 2021-01-19
Förlag: Springer Nature Switzerland AG