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:	15 Nov 2024 07:30
URI:	https://orca.cardiff.ac.uk/id/eprint/142205

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