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- Title
Energy and area minimizers in metric spaces.
- Authors
Lytchak, Alexander; Wenger, Stefan
- Abstract
We show that in the setting of proper metric spaces one obtains a solution of the classical 2-dimensional Plateau problem by minimizing the energy, as in the classical case, once a definition of area has been chosen appropriately. We prove the quasi-convexity of this new definition of area. Under the assumption of a quadratic isoperimetric inequality we establish regularity results for energy minimizers and improve Hölder exponents of some area-minimizing discs.
- Subjects
METRIC spaces; PLATEAU'S problem; ISOPERIMETRIC inequalities; CONVEX surfaces; CONVEX geometry
- Publication
Advances in Calculus of Variations, 2017, Vol 10, Issue 4, p407
- ISSN
1864-8258
- Publication type
Article
- DOI
10.1515/acv-2015-0027