{"paper":{"title":"Starshaped compact hypersurfaces with prescirbed Weingarten curvature in warped product manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AP","authors_text":"Daguang Chen, Haizhong Li, Zhizhang Wang","submitted_at":"2017-04-30T13:29:35Z","abstract_excerpt":"Given a compact Riemannian manifold $M$, we consider a warped product $\\bar M = I \\times_h M$ where $I$ is an open interval in $\\Bbb R$. For a positive function $\\psi$ defined on $\\bar M$, we generalized the arguments in \\cite{GRW2015} and \\cite{RW16}, to obtain the curvature estimates for Hessian equations $\\sigma_k(\\kappa)=\\psi(V,\\nu(V))$. We also obtain some existence results for the starshaped compact hypersurface $\\Sigma$ satisfying the above equation with various assumptions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.00313","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"}