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Twist points of the von Koch snowflake
Author(s):
Fausto
Di Biase;
Bert
Fischer;
Rüdiger
L.
Urbanke
Journal:
Proc. Amer. Math. Soc.
126
(1998),
1487-1490.
MSC (1991):
Primary 31A15, 30C35
MathSciNet review:
1443822
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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.
References:
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- 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
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- W.K. Hayman and P.B. Kennedy, Subharmonic functions, Academic Press, London, 1976. MR 57:665
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- Ch. Pommerenke, Boundary behaviour of conformal maps, Springer-Verlag, Berlin Heidelberg New York, 1992. MR 95b:30008
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- 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.
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Additional Information:
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
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