Minimal hypersurfaces and geometric inequalities

Simon Brendle

doi:10.5802/afst.1734

Simon Brendle ¹

¹ Department of Mathematics, Columbia University, New York NY 10027, USA

Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 32 (2023) no. 1, pp. 179-201.

Abstract

In this expository paper, we discuss some of the main geometric inequalities for minimal hypersurfaces. These include the classical monotonicity formula, the Alexander–Osserman conjecture, the isoperimetric inequality for minimal surfaces, and the Michael–Simon Sobolev inequality.

Received: 2020-09-30
Accepted: 2021-02-22
Published online: 2023-03-27

DOI: 10.5802/afst.1734

Author's affiliations:

Simon Brendle ¹

¹ Department of Mathematics, Columbia University, New York NY 10027, USA

License:

CC-BY 4.0

Copyrights: The authors retain unrestricted copyrights and publishing rights

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Simon Brendle. Minimal hypersurfaces and geometric inequalities. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 32 (2023) no. 1, pp. 179-201. doi : 10.5802/afst.1734. https://afst.centre-mersenne.org/articles/10.5802/afst.1734/

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