{"paper":{"title":"Covariant Schr\\\"odinger semigroups on Riemannian manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AP","math.FA","math.MP","math.PR"],"primary_cat":"math.DG","authors_text":"Batu G\\\"uneysu","submitted_at":"2018-01-04T13:09:43Z","abstract_excerpt":"This monograph develops the theory of covariant Schr\\\"odinger semigroups acting on sections of vector bundles over noncompact Riemannian manifolds from scratch.\n  Contents:\n  I. Sobolev spaces on vector bundles\n  II. Smooth heat kernels on vector bundles\n  III. Basis differential operators in Riemannian manifolds\n  IV. Some specific results for the minimal heat kernel\n  V. Wiener measure and Brownian motion on Riemannian manifolds\n  VI. Contractive Dynkin and Kato potentials\n  VII. Foundations of covariant Schr\\\"odinger semigroups\n  VIII. Compactness of $V(H^{\\nabla}+1)^{-1}$\n  IX. $L^q$-prope"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.01335","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"}