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Reifenberg’s isoperimetric inequality revisited

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Abstract

We prove a generalization of Reifenberg’s isoperimetric inequality. The main result of this paper is used in Harrison and Pugh (General methods of elliptic minimization, Available on arxiv, 2016) 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.

Mathematics Subject Classification

28A78 

Notes

References

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Mathematics DepartmentStony Brook UniversityStony BrookUSA

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