A Liouville type theorem to 2-Hessian equations

2019/06/25 by Yan He, He, Yan, Haoyang Sheng +3
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1906.10588

openalex publication_date 2019/06/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we proved that any 2-convex solution u of σ₂(D²u)=1 with a quadratic growth must be a quadratic polynomial in ℝⁿ (n≥ 3 ) by using a Pogorelov estimate and the global gradient estimate. And we give a positive answer to the unresolved issue in \citeCX.

Citations

• The Dirichlet problem for nonlinear second order elliptic equations, III: Functions of the eigenvalues of the Hessian
• Global C2‐Estimates for Convex Solutions of Curvature Equations

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