{"paper":{"title":"Diffusion semigroup on manifolds with time-dependent metrics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Li-Juan Cheng","submitted_at":"2012-11-15T14:53:04Z","abstract_excerpt":"Let $L_t:=\\Delta_t +Z_t $, $t\\in [0,T_c)$ on a differential manifold equipped with time-depending complete Riemannian metric $(g_t)_{t\\in [0,T_c)}$, where $\\Delta_t$ is the Laplacian induced by $g_t$ and $(Z_t)_{t\\in [0,T_c)}$ is a family of $C^{1,1}$-vector fields. We first present some explicit criteria for the non-explosion of the diffusion processes generated by $L_t$; then establish the derivative formula for the associated semigroup; and finally, present a number of equivalent semigroup inequalities for the curvature lower bound condition, which include the gradient inequalities, transpo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.3621","kind":"arxiv","version":3},"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"}