{"paper":{"title":"Entropy and stability of hyperbolic manifolds","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Antoine Song","submitted_at":"2023-02-15T01:49:20Z","abstract_excerpt":"Let $(M,g_0)$ be a closed oriented hyperbolic manifold of dimension at least $3$. By the volume entropy inequality of G. Besson, G. Courtois and S. Gallot, for any Riemannian metric $g$ on $M$ with same volume as $g_0$, its volume entropy $h(g)$ satisfies $h(g)\\geq n-1$ with equality only when $g$ is isometric to $g_0$. We show that the hyperbolic metric $g_0$ is stable in the following sense: if $g_i$ is a sequence of Riemaniann metrics on $M$ of same volume as $g_0$ and if $h(g_i)$ converges to $n-1$, then there are smooth subsets $Z_i\\subset M$ such that both $\\mathrm{Vol}(Z_i,g_i)$ and $\\m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2302.07422","kind":"arxiv","version":5},"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/2302.07422/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"}