Modern Approaches to Discrete Curvature: 2017

2017 | Science & Mathematics

In the recent years, a very active field of research has appeared, blending discrete mathematics, differential geometry, probabilities and computer graphics, 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, and the bridges between the two are manifold, and involve numerous fields: metric spaces, Riemannian and Euclidean geometries, geometric measure theory, topology, partial differential equations, calculus of variations, gradient flows, asymptotic analysis, probabilities, harmonic analysis, graph theory, etc. In spite of the crucial importance both in theoretical mathematics and in applications, there are, up to now, almost no books providing a coherent outlook on this emerging field. This work offers a fantastic glimpse into this rich new world and its recent developments. It shows a vertiginous collection of ideas and tools, and every reader interested in discrete curvature will learn something new.This book aims to be a meeting point not only for mathematicians and computer scientists, but also between various fields of mathematics that are usually separated.

It will be profitable both for graduate students and experts wishing to broaden their knowledge.

Laurent Najman (Author)

Pascal Romon (Author)