Conformal metrics of the ball with constant 𝜎_{𝑘}-curvature and constant boundary mean curvature

descriptionPublicationkeyboard_double_arrow_right Article 05 Mar 2026Embargo end date: 01 Jan 2025 English Publisher:American Mathematical Society (AMS)Journal:Proceedings of the American Mathematical Society (issn: 0002-9939, eissn: 1088-6826,

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Authors: Chen, Xuezhang; Wei, Wei;

doi: 10.1090/proc/17697 , 10.48550/arxiv.2504.04515

Conformal metrics of the ball with constant 𝜎_{𝑘}-curvature and constant boundary mean curvature

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Abstract

On the upper hemisphere, we use the Obata-Escobar argument to classify conformal metrics with constant $σ_k$ curvature and constant boundary mean curvature in all types of cones including positive and negative cones. This extends a result of Escobar in \cite{Es} for $k=1$.

Keywords

Differential Geometry (math.DG), FOS: Mathematics, Analysis of PDEs (math.AP)

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