Proceedings of the American Mathematical Society

Author(s): Fausto Di Biase; Bert Fischer; Rüdiger L. Urbanke
Journal: Proc. Amer. Math. Soc. 126 (1998), 1487-1490.
MSC (1991): Primary 31A15, 30C35
Retrieve article in: PDF
This article is available free of charge

Abstract: It is known that the set of twist points in the boundary of the von Koch snowflake domain has full harmonic measure. We provide a new, simple proof, based on the doubling property of the harmonic measure, and on the existence of an equivalent measure, invariant and ergodic with respect to the shift.

[C85]: L. Carleson, On the support of harmonic measure for sets of Cantor type, Ann. Acad. Sci. Fenn. Ser. AI Math 10 (1985), 113-123. MR 87b:31002
[HK76]: W.K. Hayman and P.B. Kennedy, Subharmonic functions, Academic Press, London, 1976. MR 57:665
[KW85]: R. Kaufman and J.M. Wu, On the snowflake domain, Ark. Mat. 23 (1985), 177-183. MR 86m:31002
[PTW92]: M.A. Picardello, M.H. Taibleson and W. Woess, Harmonic measure of the planar Cantor set from the viewpoint of graph theory, Discrete Math. 109 (1992), 193-202. MR 94f:31009
[P92]: Ch. Pommerenke, Boundary behaviour of conformal maps, Springer-Verlag, Berlin Heidelberg New York, 1992. MR 95b:30008
[S94]: Ya.G. Sinai, Topics in ergodic theory, Princeton University Press, Princeton, N.J., 1994. MR 95j:28017
[vK06]: H. von Koch, Une méthode géométrique élémentaire pour l'étude de certain questions de la théorie des courbes planes, Acta Math. 30 (1906), 145-174.

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 31A15, 30C35

Fausto Di Biase
Affiliation: Department of Mathematics, Princeton University, Princeton, New Jersey 08544
Email: biase@math.princeton.edu

Bert Fischer
Affiliation: Department of Mathematics, Princeton University, Princeton, New Jersey 08544
Email: fischer@math.princeton.edu

Rüdiger L. Urbanke
Affiliation: Room 2C-254, Bell Labs, Lucent Technologies, 600 Mountain Avenue, Murray Hill, New Jersey 07974
Email: ruediger@research.bell-labs.com

DOI: 10.1090/S0002-9939-98-04226-9
PII: S 0002-9939(98)04226-9
Keywords: Harmonic measure, von Koch snowflake, doubling property, shift, ergodicity, twist points
Received by editor(s): November 1, 1996
Additional Notes: The first author was supported by CNR Grants 203.01.55 and 203.01.63.
The second author was partially supported by the Alexander von Humboldt Foundation.
Communicated by: Albert Baernstein II
Copyright of article: Copyright 1998, American Mathematical Society

			Journals Home Search Author Info Subscribe Tech Support Help
ISSN 1088-6826 (e) ISSN 0002-9939 (p)

Previous issue \| Table of contents \| Next issue Articles in press \| Recently posted articles \| Most recent issue \| All issues Previous Article \| Next Article


	Comments: webmaster@ams.org © Copyright 2009, American Mathematical Society Privacy Statement		Search the AMS