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A characterization of convex calibrable sets in

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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.

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Authors and Affiliations

  1. CMLA, ENS Cachan, 61 Av. du Président Wilson, 94235, Cachan Cedex, France

    F. Alter

  2. Departament de Tecnologia, Universitat Pompeu-Fabra, Passeig de Circumvalació 8, 08003, Barcelona, Spain

    V. Caselles

  3. CEREMADE, CNRS UMR 7534, Université Paris-Dauphine, 75775, Paris Cedex 16, France

    A. Chambolle

Authors
  1. F. Alter
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  2. V. Caselles
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  3. A. Chambolle
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Correspondence to V. Caselles.

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Mathematics Subject Classification (2000): 35J70, 49J40, 52A20, 35K65

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Alter, F., Caselles, V. & Chambolle, A. A characterization of convex calibrable sets in . Math. Ann. 332, 329–366 (2005). https://doi.org/10.1007/s00208-004-0628-9

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  • DOI: https://doi.org/10.1007/s00208-004-0628-9

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