Modern Approaches to Discrete Curvature, 1st ed. 2017 Lecture Notes in Mathematics Series, Vol. 2184

 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.

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