Lipschitz regularity of the extremal distribution forces C^∞ regularity for volume-preserving partially hyperbolic diffeomorphisms on closed 3-manifolds.
Geiges.An introduction to contact topology, volume 109 ofCambridge Studies in Advanced Mathematics
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Starshaped polytopes exist in R^4 such that every starshaped smoothing of their boundary induces a Reeb flow with positive topological entropy, answering Ostrover-Ginzburg; analogous C^0 metrics on surfaces have geodesic flows with h_top > C for any smoothing.
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Extremal distributions of partially hyperbolic systems: the Lipschitz threshold
Lipschitz regularity of the extremal distribution forces C^∞ regularity for volume-preserving partially hyperbolic diffeomorphisms on closed 3-manifolds.
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Polytopes and $C^0$-Riemannian metrics with positive $h_{\rm top}$
Starshaped polytopes exist in R^4 such that every starshaped smoothing of their boundary induces a Reeb flow with positive topological entropy, answering Ostrover-Ginzburg; analogous C^0 metrics on surfaces have geodesic flows with h_top > C for any smoothing.