{"paper":{"title":"Boltzmann's Entropy and K\\\"ahler-Ricci Solitons","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Frederick Tsz-Ho Fong","submitted_at":"2016-05-25T19:29:37Z","abstract_excerpt":"We study a Boltzmann's type entropy functional (which appeared in existing literature) defined on K\\\"ahler metrics of a fixed K\\\"ahler class. The critical points of this functional are gradient K\\\"ahler-Ricci solitons, and the functional was known to be monotonically increasing along the K\\\"ahler-Ricci flow in the canonical class.\n  In this article, we derive and analyze the second variation formula for this entropy functional, and show that all gradient K\\\"ahler-Ricci solitons are stable with respect to this entropy functional. Furthermore, using this result, we give a new proof that gradient"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.08019","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"}