2012/02/29 by Jouni Parkkonen, JOUNI PARKKONEN, Frédéric Paulin +1
Mathematics · #Bundle #Curvature #Equidistant #Geodesic #Geometric Analysis and Curvature Flows #Mixing (physics) #Negative curvature #Nonlinear Partial Differential Equations #Point processes and geometric inequalities #Regular polygon #Skinning #math.DS #msc:20H10 #msc:37A25 #msc:37D40 #msc:53C40
paper · pdf · doi:10.1017/etds.2012.192
published as Ergod. Th. Dynam. Sys. 34 (2014) 1310-1342 · 32 pages. Revised version with important modifications to Section 4
arxiv created 2012/10/25 · openalex publication_date 2013/04/30 · openalex created_date 2016/06/24 · arxiv updated 2019/02/20 · openalex updated_date 2026/08/05
Abstract Let C be a locally convex closed subset of a negatively curved Riemannian manifold M . We define the skinning measure σ C on the outer unit normal bundle to C in M by pulling back the Patterson–Sullivan measures at infinity, and give a finiteness result for σ C , generalizing 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 mBM on T1 M , assuming only that mBM is finite and mixing for the geodesic flow. Under additional assumptions on the rate of mixing, we give a control on the rate of equidistribution.