{"ID":23543103,"CreatedAt":"2026-09-18T03:57:46.008101424Z","UpdatedAt":"2026-09-18T03:57:46.008101424Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2609.20445","arxiv_id":"2609.20445","title":"Rigidity for Convex Entire Solutions to the $k$-Hessian Equation","abstract":"We prove that for each $3\\le k\\le n-1$ a convex $C^2$ entire solution of $σ_k$ equation in $\\mathbb{R}^n$ with positive constant right hand side is a quadratic polynomial, without a growth assumption on the solution itself.","short_abstract":"We prove that for each $3\\le k\\le n-1$ a convex $C^2$ entire solution of $σ_k$ equation in $\\mathbb{R}^n$ with positive constant right hand side is a quadratic polynomial, without a growth assumption on the solution itself.","url_abs":"https://arxiv.org/abs/2609.20445","url_pdf":"https://arxiv.org/pdf/2609.20445v1","authors":"[\"Xingchen Zhou\",\"Ruixuan Zhu\"]","published":"2026-09-17T14:16:43Z","proceeding":"math.AP","tasks":"[\"math.AP\"]","methods":"[]","has_code":false}