August 20, 2024Open Access

C² estimates for k-Hessian equations and a rigidity theorem

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Abstract

We derive a concavity inequality for k-Hessian operators under the semi-convexity condition. As an application, we establish interior estimates for semi-convex solutions of the k-Hessian equations with vanishing Dirichlet boundary and obtain a Liouville-type result. Additionally, we provide new and simple proofs of Guan-Ren-Wang's results on global curvature estimates for k-curvature equations.

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Ruijia Zhang (Tue,) studied this question.

synapsesocial.com/papers/68e5bb23b6db6435875530cd https://doi.org/https://doi.org/10.48550/arxiv.2408.10781

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