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A fully-nonlinear flow and quermassintegral inequalities in the sphere

Chen, Chuanqiang, Guan, Pengfei, Li, Junfang and Scheuer, Julian ORCID: https://orcid.org/0000-0003-2664-1896 2022. A fully-nonlinear flow and quermassintegral inequalities in the sphere. Pure and Applied Mathematics Quarterly 18 (2) , pp. 437-461. 10.4310/PAMQ.2022.v18.n2.a4

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Abstract

This expository paper presents the current knowledge of particular fully nonlinear curvature flows with local forcing term, so-called locally constrained curvature flows. We focus on the spherical ambient space. The flows are designed to preserve a quermassintegral and to de‑/increase the other quermassintegrals. The convergence of this flow to a round sphere would settle the full set of quermassintegral inequalities for convex domains of the sphere, but a full proof is still missing. Here we collect what is known and hope to attract wide attention to this interesting problem.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Mathematics
Uncontrolled Keywords: Locally constrained curvature flows; Quermassintegral inequalities
Publisher: International Press
ISSN: 1558-8599
Date of First Compliant Deposit: 1 July 2021
Date of Acceptance: 28 June 2021
Last Modified: 17 Nov 2023 09:59
URI: https://orca.cardiff.ac.uk/id/eprint/142205

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