Reifenberg's Isoperimetric Inequality Revisited

We prove a generalization of Reifenberg's isoperimetric inequality. The main result of this paper is used to establish existence of a minimizer for an anisotropically-weighted area functional among a collection of surfaces which satisfies a set of axioms, namely being closed under certain defor...

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Bibliographic Details
Published in:arXiv.org 2018-01
Main Author: Pugh, Harrison
Format: Article
Language:English
Subjects:
Axioms
Deformation
Online Access:Get full text
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Summary:We prove a generalization of Reifenberg's isoperimetric inequality. The main result of this paper is used to establish existence of a minimizer for an anisotropically-weighted area functional among a collection of surfaces which satisfies a set of axioms, namely being closed under certain deformations and Hausdorff limits. This problem is known as the axiomatic Plateau problem.
ISSN:2331-8422