English

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}
}