Alexandrov-Fenchel inequalities for convex hypersurfaces with free boundary in a ball

Scheuer, Julian ORCID: https://orcid.org/0000-0003-2664-1896, Wang, Guofang and Xia, Chao 2022. Alexandrov-Fenchel inequalities for convex hypersurfaces with free boundary in a ball. Journal of Differential Geometry 120 (2) , pp. 345-373. 10.4310/jdg/1645207496

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Abstract

In this paper we first introduce quermassintegrals for free boundary hypersurfaces in the ( n + 1 ) -dimensional Euclidean unit ball. Then we solve some related isoperimetric type problems for convex free boundary hypersurfaces, which lead to new Alexandrov–Fenchel inequalities. In particular, for n = 2 we obtain a Minkowski-type inequality and for n = 3 we obtain an optimal Willmore-type inequality. To prove these estimates, we employ a specifically designed locally constrained inverse harmonic mean curvature flow with free boundary.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Schools > Mathematics
Publisher:	International Press
ISSN:	0022-040X
Date of First Compliant Deposit:	12 October 2020
Date of Acceptance:	19 September 2019
Last Modified:	21 Nov 2024 13:00
URI:	https://orca.cardiff.ac.uk/id/eprint/135528

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