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 of a domain is replaced by a metric , 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 , where is a Banach space and 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