Energy and area minimizers in metric spaces-Reference-Cited by-同舟云学术

Energy and area minimizers in metric spaces

Published:2017-10-01 Issue:4 Volume:10 Page:407-421
ISSN:1864-8266
Container-title:Advances in Calculus of Variations
language:
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Author:

Lytchak Alexander¹,Wenger Stefan²

Affiliation:

1. Mathematisches Institut, Universität Köln, Weyertal 86–90, 50931Köln, Germany

2. Department of Mathematics, University of Fribourg, Chemin du Musée 23, 1700Fribourg, Switzerland

Abstract

AbstractWe 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.

Funder

Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Analysis

Link

https://www.degruyter.com/document/doi/10.1515/acv-2015-0027/pdf

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