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arXiv · 2609.22447

The sharp isoperimetric inequality for varifolds in codimension two

Raphael Tsiamis
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Abstract

We prove a Michael-Simon inequality for a class of varifolds in Euclidean space that includes all integral varifolds with locally bounded first variation of arbitrary dimension and codimension. In codimension $2$, this inequality is sharp and implies the sharp isoperimetric inequality for varifolds, which attains equality precisely for the round disk. Our proof uses the optimal transportation approach of Brendle-Eichmair.

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Raphael Tsiamis. 2026-09-18. The sharp isoperimetric inequality for varifolds in codimension two. https://arxiv.org/abs/2609.22447

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