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This extends a result of H.-Q. Li for the Heisenberg group. The proof is based on pointwise heat kernel estimates, and follows an approach used by Bakry, Baudoin, Bonnefont, and Chafa\\\"i."},"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":"0904.1781","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2009-04-11T07:06:05Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"fb53333bfbd496b4caed52b865de2e8dae36636bc513de43d27a497b12d392dc","abstract_canon_sha256":"b4e5413ef2a73026990ed2b2cfa63330319240959b3dbc65ea13ce76c6c82fd8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:49:03.568589Z","signature_b64":"1cKZvU+w90tI5tnpnJ1/Qz4sEoOnOuxmd/4VzE+J2hHyY3/vdsgVK4usOSMdyGc1LoTB4CKU23QBdBnhWogBCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7972cdc95f608ee108e996a974e9a48d899ffff37ed04d391e7469d41e5ce068","last_reissued_at":"2026-05-18T02:49:03.567975Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:49:03.567975Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Gradient estimates for the subelliptic heat kernel on H-type groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AP","authors_text":"Nathaniel Eldredge","submitted_at":"2009-04-11T07:06:05Z","abstract_excerpt":"We prove the following gradient inequality for the subelliptic heat kernel on nilpotent Lie groups $G$ of H-type:\n  $$|\\nabla P_t f| \\le K P_t(|\\nabla f|)$$ where $P_t$ is the heat semigroup corresponding to the sublaplacian on $G$, $\\nabla$ is the subelliptic gradient, and $K$ is a constant. 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