C² estimates for k-Hessian equations and a rigidity theorem

2024/08/20 by Zhang, Ruijia
#35J60 #53C42 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2408.10781

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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