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SUMMARY:A varifold perspective on discrete surfaces (Université Paris-Sac
lay)
DTSTART:20210607T080000Z
DTEND:20210607T090000Z
DTSTAMP:20241004T025100Z
UID:indico-event-6446@indico.math.cnrs.fr
CONTACT:clement.sarrazin@universite-paris-saclay.fr
DESCRIPTION:Speakers: Blanche Buet\n\nJoint work with: Gian Paolo Leonardi
(Trento)\, Simon Masnou (Lyon) and Martin Rumpf (Bonn).\n\nWe propose a n
atural framework for the study of surfaces and their different discretizat
ions based on varifolds. Varifolds have been introduced by Almgren to carr
y out the study of minimal surfaces. Though mainly used in the context of
rectifiable sets\, they turn out to be well suited to the study of discret
e type objects as well.\nWhile the structure of varifold is flexible enoug
h to adapt to both regular and discrete objects\, it allows to define vari
ational notions of mean curvature and second fundamental form based on the
divergence theorem. Thanks to a regularization of these weak formulations
\, we propose a notion of discrete curvature (actually a family of discret
e curvatures associated with a regularization scale) relying only on the v
arifold structure. We prove nice convergence properties involving a natura
l growth assumption: the scale of regularization must be large with respec
t to the accuracy of the discretization. We performed numerical computatio
ns of mean curvature and Gaussian curvature on point clouds in R^3 to ill
ustrate this approach.\nBuilding on the explicit expression of approximate
mean curvature we propose\, we perform mean curvature flow of point cloud
varifolds beyond the formation of singularities and we recover well-known
soap films.\n\n \n\nhttps://indico.math.cnrs.fr/event/6446/
LOCATION:https://webconf.math.cnrs.fr/b/pau-fvx-pac (mdp 343477) (À dista
nce)
URL:https://indico.math.cnrs.fr/event/6446/
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