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On the Existence and Regularity of Mass-Minimizing Currents with an Elastic Boundary

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Abstract

We study the following variational problem. For a compact manifold S0 embedded in the Euclidean space we consider deformations of S0. They are represented by Lipschitz continuous homeomorphisms of S0 whose images are embedded manifolds. We introduce an energy of a deformation ϕ which depends on the first derivative of ϕ the curvature of ϕ(S0) and the mass of a mass minimizing current which is bounded by ϕ(S0). In this paper it is shown that an energy minimizing deformation ϕ of (S0) exists. Moreover, in the case that S0 has codimension 1, ϕ (S0) is an embedded C3a -submanifold, if ϕ is of the class C2,1.

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  1. Centre for Mathematics and its Applications, School of Mathematical Sciences, Australian National University, Canberra, ACT 0200, Australia

    Felicia Bernatzki

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  1. Felicia Bernatzki
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Bernatzki, F. On the Existence and Regularity of Mass-Minimizing Currents with an Elastic Boundary. Annals of Global Analysis and Geometry 15, 379–399 (1997). https://doi.org/10.1023/A:1006572122998

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  • DOI: https://doi.org/10.1023/A:1006572122998

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