{"paper":{"title":"Hyperbolic Alexandrov-Fenchel quermassintegral inequalities II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Guofang Wang, Jie Wu, Yuxin Ge","submitted_at":"2013-04-04T16:21:10Z","abstract_excerpt":"In this paper we first establish an optimal Sobolev type inequality for hypersurfaces in $\\H^n$(see Theorem \\ref{mainthm1}). As an application we obtain hyperbolic Alexandrov-Fenchel inequalities for curvature integrals and quermassintegrals. Precisely, we prove a following geometric inequality in the hyperbolic space $\\H^n$, which is a hyperbolic Alexandrov-Fenchel inequality, \\begin{equation*} \\begin{array}{rcl} \\ds \\int_\\Sigma \\s_{2k}\\ge \\ds\\vs C_{n-1}^{2k}\\omega_{n-1}\\left\\{\\left(\\frac{|\\Sigma|}{\\omega_{n-1}} \\right)^\\frac 1k + \\left(\\frac{|\\Sigma|}{\\omega_{n-1}} \\right)^{\\frac 1k\\frac {n-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.1417","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"}