Reifenberg's Isoperimetric Inequality Revisited
Analysis of PDEs
2018-01-23 v3
Abstract
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.
Keywords
Cite
@article{arxiv.1706.00108,
title = {Reifenberg's Isoperimetric Inequality Revisited},
author = {Harrison Pugh},
journal= {arXiv preprint arXiv:1706.00108},
year = {2018}
}