{"paper":{"title":"Heat kernels in the context of Kato potentials on arbitrary manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.MP","math.PR"],"primary_cat":"math-ph","authors_text":"Batu G\\\"uneysu","submitted_at":"2015-11-05T09:46:50Z","abstract_excerpt":"By introducing the concept of \\emph{Kato control pairs} for a given Riemannian minimal heat kernel, we prove that on every Riemannian manifold $(M,g)$ the Kato class $\\mathcal{K}(M,g)$ has a subspace of the form $\\mathsf{L}^q(M,d\\varrho)$, where $\\varrho$ has a continuous density with respect to the volume measure $\\mu_g$ (where $q$ depends on $\\dim(M)$). Using a local parabolic $\\mathsf{L}^1$-mean value inequality, we prove the existence of such densities for every Riemannian manifold, which in particular implies $\\mathsf{L}^q_{loc}(M)\\subset\\mathcal{K}_{loc}(M,g)$. Based on previously establ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.01675","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"}