EAN: 9783319580012

MODERN APPROACHES TO DISCRETE CURVATURE KARTONI...

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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