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On Isometric Extension of Moebius Maps | | Kingshook Biswas
; | | Date: |
28 Mar 2012 | | Abstract: | We consider Moebius homeomorphisms $f : partial X o partial Y$ between
boundaries of CAT(-1) spaces $X,Y$ equipped with visual metrics. We prove that
if $X,Y$ are proper and geodesically complete then $f$ extends to a $(1, log
2)$-quasi-isometry with image $1/2log 2$-dense in $Y$. We prove that if $X,Y$
are in addition metric trees then $f$ extends to a surjective isometry. The
proofs involve a study of a space $mathcal{M}(partial X)$ of metrics on
$partial X$ Moebius equivalent to a visual metric and an isometric embedding
of $X$ into $mathcal{M}(partial X)$. | | Source: | arXiv, 1203.6212 | | Services: | Forum | Review | PDF | Favorites | |
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