{"paper":{"title":"Rotational symmetry of non negatively curved expanding gradient Ricci solitons","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Alix Deruelle","submitted_at":"2013-03-14T13:45:10Z","abstract_excerpt":"Let $(M^n,g,\\nabla f)$, $n\\geq 3$, be an expanding gradient Ricci soliton with nonnegative sectional curvature whose asymptotic cone is isometric to $C(\\mathbb{S}^{n-1}(c))$ where $\\mathbb{S}^{n-1}(c)$ is the standard $(n-1)$-sphere of curvature $1/c^2$, with $c\\in(0,1)$. We prove that if the convergence to the asymptotic cone is smooth, $(M^n,g,\\nabla f)$ is rotationally symmetric. This is the expanding analogue of the Perelman conjecture on the Bryant soliton and this work is based on the proof by Brendle \\cite{Bre-Rot-3d}. This has also been proved recently by Chodosh \\cite{Cho-EGS}."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.3446","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"}