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Uniqueness of Solutions to a Class of Mixed Hessian Quotient Type Equations

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Abstract

In this paper, we investigate the uniqueness of uniformly convex solutions to geometric partial differential equations \(\frac{\sigma _k(\eta )}{\sigma _l(\eta )}=u^{p-1}\) when \(-(k-l)< p-1 <0\). The result implies that the self-similar solutions of the corresponding curvature flows converge to a round point.

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Funding

Research of the Chuanqiang Chen is supported by ZJNSF No. LXR22A010001 and NSFC No. 12171260. Research of the Lu Xu is supported by NSFC No. 12171143.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Ningbo University, Ningbo, 315211, Zhejiang, People’s Republic of China

    Chuanqiang Chen

  2. School of Mathematics, Hunan University, Changsha, 410082, Hunan, People’s Republic of China

    Lu Xu

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  1. Chuanqiang Chen
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  2. Lu Xu
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Correspondence to Lu Xu.

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Chen, C., Xu, L. Uniqueness of Solutions to a Class of Mixed Hessian Quotient Type Equations. J Geom Anal 33, 210 (2023). https://doi.org/10.1007/s12220-023-01275-0

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