A characterization of convex calibrable sets in |
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Authors: | F?Alter Email author" target="_blank">V?CasellesEmail author A?Chambolle |
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Institution: | (1) CMLA, ENS Cachan, 61 Av. du Président Wilson, 94235 Cachan Cedex, France;(2) Departament de Tecnologia, Universitat Pompeu-Fabra, Passeig de Circumvalació 8, 08003 Barcelona, Spain;(3) CEREMADE, CNRS UMR 7534, Université Paris-Dauphine, 75775 Paris Cedex 16, France |
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Abstract: | The main purpose of this paper is to characterize the calibrability of bounded convex sets in 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 consequence we describe the evolution of convex sets in by the minimizing total variation flow.Mathematics Subject Classification (2000): 35J70, 49J40, 52A20, 35K65 |
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