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- W2167333298 abstract "In this paper we show that in some cases the E.Hopf rigidity phenomenon admits quantitative interpretation. More precisely we estimate from above the measure of the set $mathcal{M}$ swept by minimal orbits. These estimates are sharp, i.e. if $mathcal{M}$ occupies the whole phase space we recover the E.Hopf rigidity. We give these estimates in two cases: the first is the case of convex billiards in the plane, sphere or hyperbolic plane. The second is the case of conformally flat Riemannian metrics on a torus. It seems to be a challenging question to understand such a quantitative bounds for Burago-Ivanov theorem." @default.
- W2167333298 created "2016-06-24" @default.
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- W2167333298 date "2014-05-01" @default.
- W2167333298 modified "2023-10-15" @default.
- W2167333298 title "Effective bounds in E.Hopf rigidity for billiards and geodesic flows" @default.
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- W2167333298 doi "https://doi.org/10.48550/arxiv.1405.0098" @default.
- W2167333298 hasPublicationYear "2014" @default.
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