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.

Title: Fernando Po o. Su presente y su porvenir. Recopilacio n de datos y noticias oficiales ... acerca de las excepcionales condiciones y grandes ventajas que para su colonizacio n ofrece esta isla. With maps.]Publisher: British Library, Historical Print EditionsThe British Library is the national library of the United Kingdom. It is one of the world's largest research libraries holding over 150 million items in all known languages and formats: books, journals, newspapers, sound recordings, patents, maps, stamps, prints and much more. Its collections include around 14 million books, along with substantial additional collections of manuscripts and historical items dating back as far as 300 BC.The HISTORY OF EUROPE collection includes books from the British Library digitised by Microsoft. This collection includes works chronicling the development of Western civilisation to the modern age. Highlights include the development of language, political and educational systems, philosophy, science, and the arts. The selection documents periods of civil war, migration, shifts in power, Muslim expansion into Central Europe, complex feudal loyalties, the aristocracy of new nations, and European expansion into the New World. ++++The below data was compiled from various identification fields in the bibliographic record of this title. This data is provided as an additional tool in helping to insure edition identification: ++++ British Library Bremo n, Luciano Mari a; 1897. 21 p.; 8 . 10164.i.12.