LEADER 04090nam 22006735 450 001 9910257381403321 005 20200704103513.0 010 $a3-319-58002-7 024 7 $a10.1007/978-3-319-58002-9 035 $a(CKB)4100000000882277 035 $a(DE-He213)978-3-319-58002-9 035 $a(MiAaPQ)EBC6288081 035 $a(MiAaPQ)EBC5592440 035 $a(Au-PeEL)EBL5592440 035 $a(OCoLC)1005986592 035 $a(PPN)220120943 035 $a(EXLCZ)994100000000882277 100 $a20171004d2017 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aModern Approaches to Discrete Curvature /$fedited by Laurent Najman, Pascal Romon 205 $a1st ed. 2017. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2017. 215 $a1 online resource (XXVI, 353 p. 80 illus., 35 illus. in color.) 225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v2184 300 $aIncludes index. 311 $a3-319-58001-9 327 $a1 The geometric meaning of curvature. Local and nonlocal aspects of Ricci curvature.- 2 Metric Curvatures Revisited - A Brief Overview --  3 Distances between datasets --  4 Inference of curvature using tubular neighborhoods -- 5 Entropic Ricci curvature for discrete spaces -- 5 Geometric and spectral consequences of curvature bounds on tesselatations --  7 The geometric spectrum of a graph and associated curvatures --  8 Discrete minimal surfaces of Koebe type --  9 Robust and Convergent Curvature and Normal Estimators with Digital Integral Invariants -- References -- List of Figures -- Index. 330 $a This book provides a valuable glimpse into discrete curvature, a rich new field of research which blends discrete mathematics, differential geometry, probability and computer graphics. It includes a vast collection of ideas and tools which will offer something new to all interested readers. Discrete geometry has arisen as much as a theoretical development as in response to unforeseen challenges coming from applications. Discrete and continuous geometries have turned out to be intimately connected. Discrete curvature is the key concept connecting them through many bridges in numerous fields: metric spaces, Riemannian and Euclidean geometries, geometric measure theory, topology, partial differential equations, calculus of variations, gradient flows, asymptotic analysis, probability, harmonic analysis, graph theory, etc. In spite of its crucial importance both in theoretical mathematics and in applications, up to now, almost no books have provided a coherent outlook on this emerging field. 410 0$aLecture Notes in Mathematics,$x0075-8434 ;$v2184 606 $aGeometry 606 $aGeometry, Algebraic 606 $aDiscrete mathematics 606 $aComputer science$xMathematics 606 $aGeometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M21006 606 $aAlgebraic Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M11019 606 $aDiscrete Mathematics$3https://scigraph.springernature.com/ontologies/product-market-codes/M29000 606 $aComputational Mathematics and Numerical Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M1400X 615 0$aGeometry. 615 0$aGeometry, Algebraic. 615 0$aDiscrete mathematics. 615 0$aComputer science$xMathematics. 615 14$aGeometry. 615 24$aAlgebraic Geometry. 615 24$aDiscrete Mathematics. 615 24$aComputational Mathematics and Numerical Analysis. 676 $a516 702 $aNajman$b Laurent$4edt$4http://id.loc.gov/vocabulary/relators/edt 702 $aRomon$b Pascal$4edt$4http://id.loc.gov/vocabulary/relators/edt 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910257381403321 996 $aModern Approaches to Discrete Curvature$92004353 997 $aUNINA