A fully-nonlinear flow and quermassintegral inequalities in the sphere

Autor:	Chen, Chuanqiang, Guan, Pengfei, Li, Junfang, Scheuer, Julian
Rok vydání:	2021
Předmět:	Mathematics - Analysis of PDEs Mathematics - Differential Geometry
Zdroj:	Pure Appl. Math. Q. 18, no. 2, (2022), p. 437-461
Druh dokumentu:	Working Paper
DOI:	10.4310/PAMQ.2022.v18.n2.a4
Popis:	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. Comment: 19 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2102.07393 Zobrazit plný text záznamu View this record from Arxiv