{"paper":{"title":"The Li-Yau Inequality and Heat Kernels on Metric Measure Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.DG"],"primary_cat":"math.MG","authors_text":"Renjin Jiang","submitted_at":"2014-05-04T11:49:17Z","abstract_excerpt":"Let $(X,d,\\mu)$ be a $RCD^\\ast(K, N)$ space with $K\\in mathbb{R}$ and $N\\in [1,\\infty)$. Suppose that $(X,d)$ is connected, complete and separable, and $\\supp \\mu=X$. We prove that the Li-Yau inequality for the heat flow holds true on $(X,d,\\mu)$ when $K\\ge 0$. A Baudoin-Garofalo inequality and Harnack inequalities for the heat flows are established on $(X,d,\\mu)$ for general $K\\in \\mathbb{R}$. Large time behaviors of heat kernels are also studied."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.0684","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"}