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Conformal Geometry and Dynamics

Published by the American Mathematical Society, the Conformal Geometry and Dynamics (ECGD) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-4173

The 2020 MCQ for Conformal Geometry and Dynamics is 0.5.

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Relatively and inner uniform domains
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by Jussi Väisälä PDF
Conform. Geom. Dyn. 2 (1998), 56-88 Request permission


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:
  • Received by editor(s): September 18, 1997
  • Received by editor(s) in revised form: April 14, 1998
  • Published electronically: August 19, 1998
  • © Copyright 1998 American Mathematical Society
  • Journal: Conform. Geom. Dyn. 2 (1998), 56-88
  • MSC (1991): Primary 30C65
  • DOI:
  • MathSciNet review: 1637079