A characterization of convex calibrable sets in IRⁿ
Chambolle, Antonin; Caselles, Vincent; Alter, François (2005), A characterization of convex calibrable sets in IRⁿ, Mathematische Annalen, 332, 2, p. 329-366. http://dx.doi.org/10.1007/s00208-004-0628-9
TypeArticle accepté pour publication ou publié
Journal nameMathematische Annalen
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Abstract (EN)The main purpose of this paper is to characterize the calibrability of bounded convex sets in IRⁿ by the mean curvature of its boundary, extending the known analogous result in dimension 2. As a by-product of our analysis we prove that any bounded convex set C of class C1,1 has a convex calibrable set K in its interior, and and for any volume V ∈ [|K|, |C|] the solution of the perimeter minimizing problem with ﬁxed volume V in the class of sets contained in C is a convex set. As a IRⁿ consequence we describe the evolution of convex sets in by the minimizing total variation ﬂow.
Subjects / KeywordsConvex sets in n dimensions; Variational methods; Degenerate elliptic equations
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