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February 2022 Alexandrov-Fenchel inequalities for convex hypersurfaces with free boundary in a ball
Julian Scheuer, Guofang Wang, Chao Xia
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J. Differential Geom. 120(2): 345-373 (February 2022). DOI: 10.4310/jdg/1645207496

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.

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Julian Scheuer. Guofang Wang. Chao Xia. "Alexandrov-Fenchel inequalities for convex hypersurfaces with free boundary in a ball." J. Differential Geom. 120 (2) 345 - 373, February 2022. https://doi.org/10.4310/jdg/1645207496

Information

Received: 2 December 2018; Accepted: 19 September 2019; Published: February 2022
First available in Project Euclid: 23 February 2022

Digital Object Identifier: 10.4310/jdg/1645207496

Subjects:
Primary: 53C21 , 53C24 , 53C44

Keywords: constrained curvature flow , free boundary hypersurface , geometric inequality , inverse curvature flow , quermassintegral

Rights: Copyright © 2022 Lehigh University

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Vol.120 • No. 2 • February 2022
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