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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…