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arXiv · 2102.07393

A fully-nonlinear flow and quermassintegral inequalities in the sphere

Chuanqiang Chen·Pengfei Guan·Junfang Li·Julian Scheuer
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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.

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Chuanqiang Chen, Pengfei Guan, Junfang Li, Julian Scheuer. 2021-02-15. A fully-nonlinear flow and quermassintegral inequalities in the sphere. https://doi.org/10.4310/pamq.2022.v18.n2.a4

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