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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 | References | Similar Articles | Additional Information

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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Additional Information

Simon Brendle
Affiliation: Department of Mathematics, Columbia University, New York, New York 10027
MR Author ID: 655348

Received by editor(s): July 26, 2019
Received by editor(s) in revised form: May 19, 2020, and September 5, 2020
Published electronically: February 18, 2021
Additional Notes: This project was supported by the National Science Foundation under grant DMS-1806190 and by the Simons Foundation.
Article copyright: © Copyright 2021 American Mathematical Society