Relatively and inner uniform domains

Väisälä, Jussi

doi:10.1090/S1088-4173-98-00022-8

Relatively and inner uniform domains

Author: Jussi Väisälä
Journal: Conform. Geom. Dyn. 2 (1998), 56-88
MSC (1991): Primary 30C65
DOI: https://doi.org/10.1090/S1088-4173-98-00022-8
Published electronically: August 19, 1998
MathSciNet review: 1637079
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Abstract: We generalize the concept of a uniform domain in Banach spaces into two directions. (1) The ordinary metric $d$ of a domain is replaced by a metric $e\ge d$, in particular, by the inner metric of the domain. (2) The uniformity condition is supposed to hold only for certain pairs of points of the domain. We consider neargeodesics and solid arcs in these domains. Applications to the boundary behavior of quasiconformal maps are given. In particular, we study maps between domains of the form $E\times B$, where $E$ is a Banach space and $B$ is a ball.

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