{"paper":{"title":"Convergence of Scalar Curvature of Long Time K\\\"ahler-Ricci Flow on K\\\"ahler Manifold","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Lei Zhang, Zhenlei Zhang","submitted_at":"2026-06-16T01:35:22Z","abstract_excerpt":"This paper is concerned with a class of the long time K\\\"ahler-Ricci flow on a compact K\\\"ahler manifold. It is shown that the uniform $\\mu$-entropy or uniform Sobolev inequality along the normalized K\\\"ahler-Ricci flow with semiample canonical bundle. As a consequence, we prove that the scalar curvature of the K\\\"ahler metrics along the normalized K\\\"ahler-Ricci flow converge to negative Kodaira dimension of the compact K\\\"ahler manifold."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.17402","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.17402/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}