{"paper":{"title":"Evolution of relative Yamabe constant under Ricci Flow","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Boris Botvinnik, Peng Lu","submitted_at":"2019-01-31T01:48:13Z","abstract_excerpt":"Let $W$ be a manifold with boundary $M$ given together with a conformal class $\\bar C$ which restricts to a conformal class $C$ on $M$. Then the relative Yamabe constant $Y_{\\bar C}(W,M;C)$ is well-defined. We study the short-time behavior of the relative Yamabe constant $Y_{[\\bar g_t]}(W,M;C)$ under the Ricci flow $\\bar g_t$ on $W$ with boundary conditions that mean curvature $H_{\\bar g_t}\\equiv 0$ and $\\bar{g}_t|_M\\in C = [\\bar{g}_0]$. In particular, we show that if the initial metric $\\bar{g}_0$ is a Yamabe metric, then, under some natural assumptions, $\\left.\\frac{d}{dt}\\right|_{t=0}Y_{[\\b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.11169","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"}