Abstract

We derive a concavity inequality for k-Hessian operators under the semiconvexity condition. As a consequence, we establish interior estimates for semiconvex solutions to the $σ_k$ equations with vanishing Dirichlet boundary conditions and obtain a Liouville-type result. This result confirms Chang and Yuan's conjecture under the superquadratic growth condition. Additionally, we present several applications in the global curvature estimates for hypersurfaces with prescribed k-curvature in the space form.

Brief biography

Ruijia Zhang is currently an assistant professor at Sun Yat-sen University. She obtained her PhD at Tsinghua University in 2023 under the supervision of Professor Haizhong Li. Her research focuses on differential geometry and geometric analysis.

Zoom meeting

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