{"paper":{"title":"On fine differentiability properties of horizons and applications to Riemannian geometry","license":"","headline":"","cross_cats":[],"primary_cat":"gr-qc","authors_text":"G.J. Galloway, J.H.G. Fu, P.T. Chrusciel, R. Howard","submitted_at":"2000-11-20T10:27:39Z","abstract_excerpt":"We study fine differentiability properties of horizons. We show that the set of end points of generators of a n-dimensional horizon H (which is included in a (n+1)-dimensional space-time M) has vanishing n-dimensional Hausdorff measure. This is proved by showing that the set of end points of generators at which the horizon is differentiable has the same property. For 1\\le k\\le n+1 we show (using deep results of Alberti) that the set of points where the convex hull of the set of generators leaving the horizon has dimension k is ``almost a C^2 manifold of dimension n+1-k'': it can be covered, up"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"gr-qc/0011067","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"}