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.

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<p> 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.</p>
1 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.
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 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.

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A unique coherent glimpse of the state-of-the-art in Discrete Curvature Of interest to both mathematicians and computer scientists A vertiginous collection of ideas and tools Includes supplementary material: sn.pub/extras Includes supplementary material: sn.pub/extras
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Produktdetaljer

ISBN
9783319580012
Publisert
2017-10-05
Utgiver
Vendor
Springer International Publishing AG
Høyde
235 mm
Bredde
155 mm
Aldersnivå
Research, P, 06
Språk
Product language
Engelsk
Format
Product format
Heftet