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Conformal Geometry and Dynamics

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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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Additional Information

Jussi Väisälä
Affiliation: Matematiikan laitos, Helsingin yliopisto, PL 4, Yliopistonkatu 5, 00014 Helsinki, Finland
Email: jvaisala@cc.helsinki.fi

DOI: https://doi.org/10.1090/S1088-4173-98-00022-8
Received by editor(s): September 18, 1997
Received by editor(s) in revised form: April 14, 1998
Published electronically: August 19, 1998
Article copyright: © Copyright 1998 American Mathematical Society

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