{"paper":{"title":"Time-analyticity of solutions to the Ricci flow","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Brett Kotschwar","submitted_at":"2012-10-10T23:10:40Z","abstract_excerpt":"In this paper, we prove that if $g(t)$ is a smooth, complete solution to the Ricci flow of uniformly bounded curvature on $M\\times[0, \\Omega]$, then the correspondence $t\\mapsto g(t)$ is real-analytic at each $t_0\\in (0, \\Omega)$. The analyticity is a consequence of classical Bernstein-type estimates on the temporal and spatial derivatives of the curvature tensor, which we further use to show that, under the above global hypotheses, for any $x_0\\in M$ and $t_0\\in (0, \\Omega)$, there exist local coordinates $x = x^i$ on a neighborhood $U\\subset M$ of $x_0$ in which the representation $g_{ij}(x,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.3083","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"}