{"paper":{"title":"Hyperbolic Alexandrov-Fenchel quermassintegral inequalities I","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Guofang Wang, Jie Wu, Yuxin Ge","submitted_at":"2013-03-07T15:17:51Z","abstract_excerpt":"In this paper we prove the following geometric inequality in the hyperbolic space $\\H^n$ ($n\\ge 5)$, which is a hyperbolic Alexandrov-Fenchel inequality, \\[\\begin{array}{rcl} \\ds \\int_\\Sigma \\s_4 d \\mu\\ge \\ds\\vs C_{n-1}^4\\omega_{n-1}\\left\\{\\left(\\frac{|\\Sigma|}{\\omega_{n-1}} \\right)^\\frac 12 + \\left(\\frac{|\\Sigma|}{\\omega_{n-1}} \\right)^{\\frac 12\\frac {n-5}{n-1}} \\right\\}^2, \\end{array}\\] provided that $\\Sigma$ is a horospherical convex hypersurface. Equality holds if and only if $\\Sigma$ is a geodesic sphere in $\\H^n$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.1714","kind":"arxiv","version":2},"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"}