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- W2768045105 abstract "Given a Moebius homeomorphism $f : partial X to partial Y$ between boundaries of proper, geodesically complete CAT(-1) spaces $X,Y$, and a family of probability measures ${ mu_x }_{x in X}$ on $partial X$, we describe a continuous family of extensions ${hat{f}_p : X to Y }_{1 leq p leq infty}$ of $f$, called the hyperbolic $p$-barycenter maps of $f$. If all the measures $mu_x$ have full support then for $p = infty$ the map $hat{f}_{infty}$ coincides with the circumcenter map $hat{f}$ defined previously in cite{biswas5}. We use this to show that if $X, Y$ are complete, simply connected manifolds with sectional curvatures $K$ satisfying $-b^2 leq K leq -1$, then the circumcenter maps of $f$ and $f^{-1}$ are $sqrt{b}$-bi-Lipschitz homeomorphisms which are inverses of each other. It follows that closed negatively curved manifolds with the same marked length spectrum are bi-Lipschitz homeomorphic." @default.
- W2768045105 created "2017-11-17" @default.
- W2768045105 creator A5010133670 @default.
- W2768045105 date "2017-11-06" @default.
- W2768045105 modified "2023-09-27" @default.
- W2768045105 title "Hyperbolic $p$-barycenters, circumcenters, and Moebius maps" @default.
- W2768045105 cites W1599001834 @default.
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