Mathematics – Dynamical Systems
Scientific paper
2012-02-28
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.
Parkkonen Jouni
Paulin Frédéric
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