LEADER 02883oam 2200505 450 001 996466564003316 005 20210618200641.0 010 $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 $a20210618d2021 uy 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 $emaximum and compact support principles and detours on manifolds /$fBruno Bianchini [and three others] 205 $a1st ed. 2021. 210 1$aCham, Switzerland :$cBirkhäuser,$d[2021] 210 4$d©2021 215 $a1 online resource (X, 286 p. 1 illus.) 225 1 $aFrontiers in Mathematics,$x1660-8046 311 $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,$x1660-8046 606 $aRiemannian manifolds 606 $aGeometric analysis 606 $aDifferential equations, Elliptic 615 0$aRiemannian manifolds. 615 0$aGeometric analysis. 615 0$aDifferential equations, Elliptic. 676 $a516.373 700 $aBianchini$b Bruno$f1958-$01124954 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bUtOrBLW 906 $aBOOK 912 $a996466564003316 996 $aGeometric analysis of quasilinear inequalities on complete manifolds$92830646 997 $aUNISA