Year: 2026
Type: preprint
Abstract: We study the rigidity of convex entire solutions to sum Hessian equations. Using a dimension-lifting identity, we reduce the problem to a standard \(k\)-Hessian equation in one higher dimension. By applying existing rigidity theorems, we prove that every \(C^2\) convex entire solution is a quadratic polynomial for \(2\leq k\leq n\), \(α\geq0\), and a positive constant right-hand side, without any growth assumption at infinity. We also discuss the linear case \(k=1\).
Source: arXiv (Cornell University)
Authors: Ren, Changyu, Sun, Xianlu
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: Hessian加法方程及相关加法曲率方程的研究
OpenAlex ID: W7223988900