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UID:ff3e37a0-9e4a-4e96-bdb8-373e3b203668@nexttoyou
DTSTAMP:20261106T171945Z
DTSTART:20261118T200000Z
DTEND:20261118T205000Z
SUMMARY:Analysis Seminar
LOCATION:Ayres Hall 113\, 1403 Circle Drive\, Knoxville\, TN 37996
DESCRIPTION:Speaker: Fotis Ioannidis\nTitle: Quasiconformal uniformization
  and extension for planar trees\nAbstract: A quasiconformal uniformizatio
 n theorem of Rickman \\cite{Rickman} asserts that every bounded turning p
 lanar arc is the image of the unit segment under a quasiconformal self-ma
 p of the plane. We prove an analogous uniformization theorem for planar t
 rees by showing that every planar quasiconformal tree with uniform branch
  separation is quasiconformally equivalent to a quasiconvex planar tree w
 ith uniform branch separation and Hausdorff dimension arbitrarily close t
 o 1. Along the way\, we show that every quasisymmetric (resp. bi-Lipschit
 z) homeomorphism between planar quasiconformal trees that respects the co
 unterclockwise orientation of the branches at every branch point can be e
 xtended quasisymmetrically (resp. bi-Lipschitz) to the whole plane. As a 
 corollary of the extension theorem we construct a class of quadrivalent q
 uasiconformal trees\, which includes the Vicsek fractal\, so that each tr
 ee in this class is the Julia set of a uniformly quasiregular map of $\\m
 athbb{R}^2$.\n\nhttp://next-to-u.app/events/ff3e37a0-9e4a-4e96-bdb8-373e3
 b203668
URL:http://next-to-u.app/events/ff3e37a0-9e4a-4e96-bdb8-373e3b203668
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