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We prove that under some further assumptions (satisfying by a large classes of $P$ and $M$) the positive minimal heat kernels of $P-V$ and of $P$ on $M$ are equivalent. Moreover, the parabolic Martin boundary is stable under such perturbations, and the cones of all nonnegative solutions of the correspondin"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1606.08601","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-06-28T08:19:15Z","cross_cats_sorted":[],"title_canon_sha256":"ab1d65443acc394c00a90c6c0b35ccd74164197e655b985a978edbfa48b977f5","abstract_canon_sha256":"a48df42d3217c56a186be24e4e3e470177c36e2fe6bf5e6871b38c34a7ffe213"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:40:51.676498Z","signature_b64":"9RQJDLvUawq4C9nUD3wQQaBc0dneIhQ0rSUEjOo1w60rEfu7xxN4uhYbWu/gYOxHs9Haf8ZzpJgNdbG2xZjxCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3b8ed9b1831869b77d7a70274f58322ed3dcb9f3c297722d0a68b6e22372113f","last_reissued_at":"2026-05-18T00:40:51.674939Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:40:51.674939Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Equivalence of Heat Kernels of Second-order parabolic operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Debdip Ganguly, Yehuda Pinchover","submitted_at":"2016-06-28T08:19:15Z","abstract_excerpt":"Let $P$ be a second-order, symmetric, and nonnegative elliptic operator with real coefficients defined on noncompact Riemannian manifold $M$, and let $V$ be a real valued function which belongs to the class of {\\em small perturbation potentials} with respect to the heat kernel of $P$ in $M$. 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