Teichm\"uller's problem for Gromov hyperbolic domains

DOI10.1007/S11856-022-2352-0arXiv2010.11542WikidataQ115601868 ScholiaQ115601868MaRDI QIDQ6351969

Author name not available (Why is that?)

Publication date: 22 October 2020

Abstract: Let

m a t h c a l T_{K} (D)

be the class of

K

-quasiconformal automorphisms of a domain

D s u b s e t n e q m a t h b b R^{n}

with identity boundary values. Teichm"uller's problem is to determine how far a given point

x i n D

can be mapped under a mapping

f i n m a t h c a l T_{K} (D)

. We estimate this distance between

x

and

f (x)

from the above by using two different metrics, the distance ratio metric and the quasihyperbolic metric. We study Teichm"{u}ller's problem for Gromov hyperbolic domains in

m a t h b b R^{n}

with identity values at the boundary of infinity. As applications, we obtain results on Teichm"{u}ller's problem for

p s i

-uniform domains and inner uniform domains in

m a t h b b R^{n}

.

Mathematics Subject Classification ID

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