{"paper":{"title":"New differential Harnack inequalities for nonlinear heat equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Jia-Yong Wu","submitted_at":"2018-03-28T13:59:56Z","abstract_excerpt":"We prove constrained trace, matrix and constrained matrix Harnack inequalities for the nonlinear heat equation $\\omega_t=\\Delta\\omega+a\\omega\\ln \\omega$ on closed manifolds. We also derive a new interpolated Harnack inequality for the equation $\\omega_t=\\Delta\\omega-\\omega\\ln\\omega+\\varepsilon R\\omega$ on closed surfaces under the $\\varepsilon$-Ricci flow. Finally we prove a new differential Harnack inequality for the equation $\\omega_t=\\Delta\\omega-\\omega\\ln\\omega$ under the Ricci flow without any curvature condition. Among these Harnack inequalities, the correction terms are all time-exponen"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.10622","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"}