{"paper":{"title":"Partial result of Yau's Conjecture of the first eigenvalue in unit sphere $\\mathbb{S}^{n+1}(1)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Zhongyang Sun","submitted_at":"2016-07-28T03:39:27Z","abstract_excerpt":"In this paper, we partially solve Yau' Conjecture of the first eigenvalue of an embedded compact minimal hypersurface of unit sphere $\\mathbb{S}^{n+1}(1)$, i.e., Corollary 1.2. In particular, Corollary 1.3 proves that the condition $\\int_{\\Omega_{1}}|\\nabla u|^{2}=(n+1)\\int_{\\Omega_{1}}u^{2}$ is naturally true and meaningful in Corollary 1.2."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.08306","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"}