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020 _a9783319580029
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024 7 _a10.1007/978-3-319-58002-9
_2doi
050 4 _aQA440-699
072 7 _aPBM
_2bicssc
072 7 _aMAT012000
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082 0 4 _a516
_223
245 1 0 _aModern Approaches to Discrete Curvature
_h[electronic resource] /
_cedited by Laurent Najman, Pascal Romon.
250 _a1st ed. 2017.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Springer,
_c2017.
300 _aXXVI, 353 p. 80 illus., 35 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
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490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v2184
505 0 _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.
520 _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.
650 0 _aGeometry.
650 0 _aAlgebraic geometry.
650 0 _aDiscrete mathematics.
650 0 _aComputer mathematics.
650 1 4 _aGeometry.
_0https://scigraph.springernature.com/ontologies/product-market-codes/M21006
650 2 4 _aAlgebraic Geometry.
_0https://scigraph.springernature.com/ontologies/product-market-codes/M11019
650 2 4 _aDiscrete Mathematics.
_0https://scigraph.springernature.com/ontologies/product-market-codes/M29000
650 2 4 _aComputational Mathematics and Numerical Analysis.
_0https://scigraph.springernature.com/ontologies/product-market-codes/M1400X
700 1 _aNajman, Laurent.
_eeditor.
_4edt
_4http://id.loc.gov/vocabulary/relators/edt
700 1 _aRomon, Pascal.
_eeditor.
_4edt
_4http://id.loc.gov/vocabulary/relators/edt
710 2 _aSpringerLink (Online service)
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783319580012
776 0 8 _iPrinted edition:
_z9783319580036
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v2184
856 4 0 _uhttps://doi.org/10.1007/978-3-319-58002-9
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