{"paper":{"title":"Skinning measures in negative curvature and equidistribution of equidistant submanifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Fr\\'ed\\'eric Paulin, Jouni Parkkonen","submitted_at":"2012-02-28T22:08:59Z","abstract_excerpt":"Let C be a locally convex subset of a negatively curved Riemannian manifold M. We define the skinning measure on the outer unit normal bundle to C in M by pulling back the Patterson-Sullivan measures at infinity, and give a finiteness result of skinning measures, generalising the work of Oh and Shah, with different methods. We prove that the skinning measures, when finite, of the equidistant hypersurfaces to C equidistribute to the Bowen-Margulis measure on the unit tangent bundle of M, assuming only that the Bowen-Margulis measure is finite and mixing for the geodesic flow. Under additional a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.6398","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"}