Remote Access Conformal Geometry and Dynamics
Green Open Access

Conformal Geometry and Dynamics

ISSN 1088-4173



Holes and maps of Euclidean domains

Author: Jussi Väisälä
Journal: Conform. Geom. Dyn. 12 (2008), 58-66
MSC (2000): Primary 30C65
Published electronically: March 13, 2008
MathSciNet review: 2385408
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We study the behavior of the quasiconvexity and bounded turning of holes of domains under quasisymmetric and bilipschitz maps.

References [Enhancements On Off] (What's this?)

  • [GNV] M. Ghamsari, R. Näkki and J. Väisälä, John disks and extension of maps, Monatsh. Math. 117 (1994), 63-94. MR 1266774 (95e:30023)
  • [HH] H. Hakobyan and D.A. Herron, Euclidean quasiconvexity, Ann. Acad. Sci. Fenn. Math. 33 (2008), 205-230.
  • [HY] J.G. Hocking and G.S. Young, Topology, Academic Press, 1959.
  • [NV] R. Näkki and J. Väisälä, John disks, Expo. Math. 9 (1991), 3-43. MR 1101948 (92i:30021)
  • [Ne] M.H.A. Newman, Elements of the topology of plane sets of points, Cambridge University Press, 1951. MR 0044820 (13:483a)
  • [TV] P. Tukia and J. Väisälä, Quasisymmetric embeddings of metric spaces, Ann. Acad. Sci. Fenn. Math. 5, 1980, 97-114. MR 595180 (82g:30038)
  • [Vä1] J. Väisälä, Quasiconformal maps of cylindrical domains, Acta Math. 162 (1989), 201-225. MR 989396 (90f:30034)
  • [Vä2] J. Väisälä, Metric duality in euclidean spaces, Math. Scand. 80 (1997), 249-288. MR 1481106 (98i:55001)

Similar Articles

Retrieve articles in Conformal Geometry and Dynamics of the American Mathematical Society with MSC (2000): 30C65

Retrieve articles in all journals with MSC (2000): 30C65

Additional Information

Jussi Väisälä
Affiliation: Matematiikan Laitos, Helsingin Yliopisto, Helsinki, Finland

Keywords: Quasisymmetric, bilipschitz, bounded turning, quasiconvex
Received by editor(s): November 13, 2007
Published electronically: March 13, 2008
Article copyright: © Copyright 2008 American Mathematical Society

American Mathematical Society