The isoperimetric inequality for a minimal submanifold in Euclidean space

Brendle, Simon

doi:10.1090/jams/969

The isoperimetric inequality for a minimal submanifold in Euclidean space
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by Simon Brendle

J. Amer. Math. Soc. 34 (2021), 595-603

DOI: https://doi.org/10.1090/jams/969

Published electronically: February 18, 2021

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Abstract:

We prove a Sobolev inequality which holds on submanifolds in Euclidean space of arbitrary dimension and codimension. This inequality is sharp if the codimension is at most $2$. As a special case, we obtain a sharp isoperimetric inequality for minimal submanifolds in Euclidean space of codimension at most $2$.

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