{"paper":{"title":"The Ricci Flow on Domains in Cohomogeneity One Manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AP","authors_text":"Artem Pulemotov","submitted_at":"2014-10-28T03:35:22Z","abstract_excerpt":"Suppose $G$ is a compact Lie group, $H$ is a closed subgroup of $G$, and the homogeneous space $G/H$ is connected. The paper investigates the Ricci flow on a manifold $M$ diffeomorphic to $[0,1]\\times G/H$. First, we prove a short-time existence and uniqueness theorem for a $G$-invariant solution $g(t)$ satisfying the boundary condition $\\mathop{\\mathrm{II}}(g(t))=F(t,g_{\\partial M}(t))$ and the initial condition $g(0)=\\hat g$. Here, $\\mathop{\\mathrm{II}}(g(t))$ is the second fundamental form of $\\partial M$, $g_{\\partial M}$ is the metric induced on $\\partial M$ by $g(t)$, $F$ is a smooth map"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.7505","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"}