{"paper":{"title":"A gap theorem for positive Einstein metrics on the four-sphere","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Harish Seshadri, Hisaaki Endo, Kazuo Akutagawa","submitted_at":"2018-01-31T05:29:24Z","abstract_excerpt":"We show that there exists a universal positive constant $\\varepsilon_0 > 0$ with the following property: Let $g$ be a positive Einstein metric on $S^4$. If the Yamabe constant of the conformal class $[g]$ satisfies\n  $$ Y(S^4, [g]) >\\frac{1}{\\sqrt{3}} Y(S^4, [g_{\\mathbb S}]) - \\varepsilon_0 $$ where $g_{\\mathbb S}$ denotes the standard round metric on $S^4$, then, up to rescaling, $g$ is isometric to $g_{\\mathbb S}$.\n  This is an extension of Gursky's gap theorem for positive Einstein metrics on the four-sphere."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.10305","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"}