{"paper":{"title":"Stochastic Analysis on Path Space over Time-Inhomogeneous Manifolds with Boundary","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Lijuan Cheng","submitted_at":"2012-11-15T15:00:38Z","abstract_excerpt":"Let $L_t:=\\Delta_t+Z_t$ for a $C^{1,1}$-vector field $Z$ on a differential manifold $M$ with possible boundary $\\partial M$, where $\\Delta_t$ is the Laplacian induced by a time dependent metric $g_t$ differentiable in $t\\in [0,T_c)$. We first introduce the damp gradient operator, defined on the path space with reference measure $\\mathbb{P}$, the law of the (reflecting) diffusion process generated by $L_t$ on the base manifold; then establish the integration by parts formula for underlying directional derivatives and prove the log-Sobolev inequality for the associated Dirichlet form, which is f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.3625","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"}