{"paper":{"title":"A Pogorelov estimate and a Liouville type theorem to parabolic $k$-Hessian equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Haoyang Sheng, Ni Xiang, Yan He","submitted_at":"2019-07-16T13:54:03Z","abstract_excerpt":"We consider Pogorelov type estimates and Liouville type theorems to parabolic $k$-Hessian equations of the form $-u_t \\sigma_k (D^2u) =1$ in $\\mathbb{R}^n\\times (-\\infty, 0]$. We derive that any \\textbf{$k+1$-convex-monotone} solution to $-u_t \\sigma_k (D^2u) =1$ when $u(x,0)$ satisfies a quadratic growth and $0<m_1\\le -u_t\\le m_2$ must be a linear function of $t$ plus a quadratic polynomial of $x$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.07006","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}