{"paper":{"title":"Remarks on Li-Yau inequality on graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.DG","authors_text":"Bin Qian","submitted_at":"2013-11-14T02:33:00Z","abstract_excerpt":"In this paper, we study Li-Yau gradient estimates for the solutions $u$ to the heat equation $\\partial_tu=\\Delta u$ on graphs under the curvature condition $CD(n,-K)$ introduced by Bauer et al. in \\cite{BHLLMY}. As applications, we derive Harnack inequalities and heat kernel estimates on graphs. Also we present a type of Hamilton gradient estimates."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.3367","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"}