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

Author: Simon Brendle
Journal: J. Amer. Math. Soc. 34 (2021), 595-603
MSC (2020): Primary 53A07, 53A10
DOI: https://doi.org/10.1090/jams/969
Published electronically: February 18, 2021
MathSciNet review: 4280868
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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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