Geometric Analysis of Quasilinear Inequalities on Complete Manifolds: Maximum and Compact Support Principles and Detours on Manifolds

· Springer Nature
电子书
286

关于此电子书

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.

为此电子书评分

欢迎向我们提供反馈意见。

如何阅读

智能手机和平板电脑
只要安装 AndroidiPad/iPhone 版的 Google Play 图书应用,不仅应用内容会自动与您的账号同步,还能让您随时随地在线或离线阅览图书。
笔记本电脑和台式机
您可以使用计算机的网络浏览器聆听您在 Google Play 购买的有声读物。
电子阅读器和其他设备
如果要在 Kobo 电子阅读器等电子墨水屏设备上阅读,您需要下载一个文件,并将其传输到相应设备上。若要将文件传输到受支持的电子阅读器上,请按帮助中心内的详细说明操作。