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On the singular set of the geodesic flow on nonpositively curved surfaces
We prove that the singular locus of the geodesic flow on the unit tangent bundle of a nonpositively curved surface enjoys an additional regularity property: its characteristic function belongs to the geometric anisotropic Sobolev space $H^{5/8-}_xH^{-13/16}_θ$. In particular, this implies that if th
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