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Circumcenter extension of Moebius maps to CAT(-1) spaces | Kingshook Biswas
; | Date: |
26 Sep 2017 | Abstract: | Given a Moebius homeomorphism $f : partial X o partial Y$ between
boundaries of proper, geodesically complete CAT(-1) spaces $X,Y$, we describe
an extension $hat{f} : X o Y$ of $f$, called the circumcenter map of $f$,
which is constructed using circumcenters of expanding sets. The extension
$hat{f}$ is shown to be a $(1, log 2)$-quasi-isometry. If in addition $X,Y$
are manifolds with curvature bounded below by $-b^2$ for some $b geq 1$ then
the extension $hat{f} : X o Y$ is a $(1, (1 - frac{1}{b})log
2)$-quasi-isometry. Circumcenter extension of Moebius maps is natural with
respect to composition with isometries. | Source: | arXiv, 1709.9110 | Services: | Forum | Review | PDF | Favorites |
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