LEADER 02958nam 22004935 450 001 9910483651503321 005 20251113204757.0 010 $a3-030-62704-7 024 7 $a10.1007/978-3-030-62704-1 035 $a(CKB)4100000011726368 035 $a(DE-He213)978-3-030-62704-1 035 $a(MiAaPQ)EBC6458927 035 $a(PPN)253253217 035 $a(EXLCZ)994100000011726368 100 $a20210118d2021 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aGeometric Analysis of Quasilinear Inequalities on Complete Manifolds $eMaximum and Compact Support Principles and Detours on Manifolds /$fby Bruno Bianchini, Luciano Mari, Patrizia Pucci, Marco Rigoli 205 $a1st ed. 2021. 210 1$aCham :$cSpringer International Publishing :$cImprint: Birkhäuser,$d2021. 215 $a1 online resource (X, 286 p. 1 illus.) 225 1 $aFrontiers in Mathematics,$x1660-8054 311 08$a3-030-62703-9 320 $aIncludes bibliographical references and index. 330 $aThis book demonstrates the influence of geometry on the qualitative behaviour of solutions of quasilinear PDEs on Riemannian manifolds. Motivated by examples arising, among others, from the theory of submanifolds, the authors study classes of coercive elliptic differential inequalities on domains of a manifold M with very general nonlinearities depending on the variable x, on the solution u and on its gradient. The book highlights the mean curvature operator and its variants, and investigates the validity of strong maximum principles, compact support principles and Liouville type theorems. In particular, it identifies sharp thresholds involving curvatures or volume growth of geodesic balls in M to guarantee the above properties under appropriate Keller-Osserman type conditions, which are investigated in detail throughout the book, and discusses the geometric reasons behind the existence of such thresholds. Further, the book also provides a unified review of recent results in the literature, and creates a bridge with geometry by studying the validity of weak and strong maximum principles at infinity, in the spirit of Omori-Yau?s Hessian and Laplacian principles and subsequent improvements. 410 0$aFrontiers in Mathematics,$x1660-8054 606 $aGlobal analysis (Mathematics) 606 $aManifolds (Mathematics) 606 $aGlobal Analysis and Analysis on Manifolds 615 0$aGlobal analysis (Mathematics). 615 0$aManifolds (Mathematics). 615 14$aGlobal Analysis and Analysis on Manifolds. 676 $a516.373 700 $aBianchini$b Bruno$f1958-$01124954 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910483651503321 996 $aGeometric analysis of quasilinear inequalities on complete manifolds$92830646 997 $aUNINA