{"paper":{"title":"A generalized maximal diameter sphere theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Nathaphon Boonnam","submitted_at":"2016-07-18T10:53:53Z","abstract_excerpt":"We prove that if a complete connected $n$-dimensional Riemannian manifold $M$ has radial sectional curvature at a base point $p\\in M$ bounded from below by the radial curvature function of a two-sphere of revolution $\\widetilde M$ belonging to a certain class, then the diameter of $M$ does not exceed that of $\\widetilde M.$ Moreover, we prove that if the diameter of $M$ equals that of $\\widetilde M,$ then $M$ is isometric to the $n$-model of $\\widetilde M.$ The class of a two-sphere of revolution employed in our main theorem is very wide. For example, this class contains both ellipsoids of pro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.05011","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"}