LEADER 04282nam 22007095 450 001 9910254082503321 005 20220413183903.0 010 $a3-319-24337-3 024 7 $a10.1007/978-3-319-24337-5 035 $a(CKB)3710000000596692 035 $a(EBL)4406563 035 $a(SSID)ssj0001653640 035 $a(PQKBManifestationID)16432944 035 $a(PQKBTitleCode)TC0001653640 035 $a(PQKBWorkID)14982858 035 $a(PQKB)11103326 035 $a(DE-He213)978-3-319-24337-5 035 $a(MiAaPQ)EBC4406563 035 $a(PPN)19222199X 035 $a(EXLCZ)993710000000596692 100 $a20160213d2016 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aMaximum principles and geometric applications /$fby Luis J. Alías, Paolo Mastrolia, Marco Rigoli 205 $a1st ed. 2016. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2016. 215 $a1 online resource (594 p.) 225 1 $aSpringer Monographs in Mathematics,$x1439-7382 300 $aDescription based upon print version of record. 311 $a3-319-24335-7 320 $aIncludes bibliographical references and index. 327 $aA crash course in Riemannian geometry -- The Omori-Yau maximum principle -- New forms of the maximum principle -- Sufficient conditions for the validity of the weak maximum principle -- Miscellany results for submanifolds -- Applications to hypersurfaces -- Hypersurfaces in warped products -- Applications to Ricci Solitons -- Spacelike hypersurfaces in Lorentzian spacetimes. 330 $aThis monograph presents an introduction to some geometric and analytic aspects of the maximum principle. In doing so, it analyses with great detail the mathematical tools and geometric foundations needed to develop the various new forms that are presented in the first chapters of the book. In particular, a generalization of the Omori-Yau maximum principle to a wide class of differential operators is given, as well as a corresponding weak maximum principle and its equivalent open form and parabolicity as a special stronger formulation of the latter.  In the second part, the attention focuses on a wide range of applications, mainly to geometric problems, but also on some analytic (especially PDEs) questions including: the geometry of submanifolds, hypersurfaces in Riemannian and Lorentzian targets, Ricci solitons, Liouville theorems, uniqueness of solutions of Lichnerowicz-type PDEs and so on. Maximum Principles and Geometric Applications is written in an easy style making it accessible to beginners. The reader is guided with a detailed presentation of some topics of Riemannian geometry that are usually not covered in textbooks. Furthermore, many of the results and even proofs of known results are new and lead to the frontiers of a contemporary and active field of research. 410 0$aSpringer Monographs in Mathematics,$x1439-7382 606 $aGlobal analysis (Mathematics) 606 $aManifolds (Mathematics) 606 $aDifferential equations, Partial 606 $aGeometry 606 $aGlobal Analysis and Analysis on Manifolds$3https://scigraph.springernature.com/ontologies/product-market-codes/M12082 606 $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155 606 $aGeometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M21006 615 0$aGlobal analysis (Mathematics) 615 0$aManifolds (Mathematics) 615 0$aDifferential equations, Partial. 615 0$aGeometry. 615 14$aGlobal Analysis and Analysis on Manifolds. 615 24$aPartial Differential Equations. 615 24$aGeometry. 676 $a510 700 $aAlías$b Luis J$4aut$4http://id.loc.gov/vocabulary/relators/aut$0755971 702 $aMastrolia$b Paolo$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aRigoli$b Marco$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910254082503321 996 $aMaximum Principles and Geometric Applications$92053520 997 $aUNINA