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

Wei Wei; Xuezhang Chen

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

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arxiv 2504.04515 v2 pith:SZWSS3KS submitted 2025-04-06 math.DG math.AP

Xuezhang Chen , Wei Wei This is my paper · ORCID

classification math.DGmath.AP

keywords constantcurvatureboundaryconesconformalmeanmetricssigma

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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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