Skinning measures in negative curvature and equidistribution of equidistant submanifolds

Details Skinning measures in negative curvature and equidistribution of equidistant submanifolds Skinning measures in negative curvature and equidistribution of equidistant submanifolds

2012-02-28

arxiv.org/abs/1202.6398v1

Mathematics

Dynamical Systems

29 pages

Scientific paper

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 Patterson-Sullivan's measures at infinity, and give a finiteness result of skinning measures, generalising the work of Oh and Shah, with different methods. When finite, we prove that the skinning measures of the equidistant hypersurfaces to C equidistribute to the Bowen-Margulis measure on the unit tangent bundle of M, assuming only it 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.

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