Titlebook: Geometric Analysis of Quasilinear Inequalities on Complete Manifolds; Maximum and Compact Bruno Bianchini,Luciano Mari,Marco Rigoli Book 2

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Book 2021of 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 improv

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1660-8046 s 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 improv978-3-030-62703-4978-3-030-62704-1Series ISSN 1660-8046 Series E-ISSN 1660-8054

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Bruno Bianchini,Luciano Mari,Marco RigoliInvestigates 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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https://doi.org/10.1057/9780230523364We briefly recall some facts from Riemannian Geometry, mostly to fix notation and conventions. Our main source for the present chapter is P. Petersen’s book. Let (.., 〈 , 〉) be a connected Riemannian manifold. We denote with ? the Levi–Civita connection induced by 〈 , 〉, and with . the (4, 0) curvature tensor of ?, with the usual sign agreement

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Representations of Internal States,The proof of some of our main results, for instance the (CSP), relies on the construction of a suitable radial solution of (..) or (..) to be compared with a given one. For convenience, hereafter we extend . to an odd function on all of . by setting

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Discourse and Diversionary JusticeIn this section, we collect two comparison theorems and a “pasting lemma” for Lip. solutions that will be repeatedly used in the sequel. Throughout the section, we assume

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Monica Heller,Mireille McLaughlinThe aim of this section is to prove Theorem . in the Introduction. We observe that the argument is based on the existence of what we call a “Khas’minskii potential”, according to the following.