Conformal metrics of the ball with constant $\sigma_k$-curvature and constant boundary mean curvature

Xuezhang Chen; Wei Wei

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arXiv · 2504.04515

Conformal metrics of the ball with constant $\sigma_k$-curvature and constant boundary mean curvature

Xuezhang Chen·Wei Wei

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Abstract

On the upper hemisphere, we use the Obata-Escobar argument to classify conformal metrics with constant $\sigma_k$ 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 $k=1$.

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BibTeX RIS

Xuezhang Chen, Wei Wei. 2025-04-06. Conformal metrics of the ball with constant $\sigma_k$-curvature and constant boundary mean curvature. https://arxiv.org/abs/2504.04515

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