3 papers
math.FA2019
Quasi-continuous vector fields on RCD spaces
Clément Debin, Nicola Gigli, Enrico Pasqualetto
In the existing language for tensor calculus on RCD spaces, tensor fields are only defined m-a.e.. In this paper we introduce the concept of tensor field defined `2-capacity-a.e.'…
math.DG2018
Hyperbolic geometry of shapes of convex bodies
Clément Debin, François Fillastre
We use the intrinsic area to define a distance on the space of homothety classes of convex bodies in the -dimensional Euclidean space, which makes it isometric to a convex subse…
math.DG2016
A compactness theorem for surfaces with Bounded Integral Curvature
Clément Debin
We prove a compactness theorem for metrics with Bounded Integral Curvature on a fixed closed surface . As a corollary, we obtain a compactification of the space of Riemannian me…