English

Pogorelov type $C^2$ estimates for Sum Hessian equations and a rigidity theorem

Analysis of PDEs 2022-04-08 v1

Abstract

We mainly study Pogorelov type C2C^2 estimates for solutions to the Dirichlet problem of Sum Hessian equations. We establish respectively Pogorelov type C2C^2 estimates for kk-convex solutions and admissible solutions under some conditions. Furthermore, we apply such estimates to obtain a rigidity theorem for kk-convex solutions of Sum Hessian equations in Euclidean space.

Keywords

Cite

@article{arxiv.2204.03135,
  title  = {Pogorelov type $C^2$ estimates for Sum Hessian equations and a rigidity theorem},
  author = {Yue Liu and Changyu Ren},
  journal= {arXiv preprint arXiv:2204.03135},
  year   = {2022}
}

Comments

27 pages

R2 v1 2026-06-24T10:40:33.660Z