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Note on arc-length and harmonic measure


Author: John S. Spraker
Journal: Proc. Amer. Math. Soc. 105 (1989), 664-665
MSC: Primary 30C35; Secondary 30C85, 30D55, 31A15
DOI: https://doi.org/10.1090/S0002-9939-1989-0956000-1
MathSciNet review: 956000
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Abstract: In this note it is shown that the only Smirnov domain for which arc-length measure is harmonic measure is the disk. The proof depends on some facts about inner and outer functions and arc-length preserving maps.


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

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  • [3] M. V. Keldysh and M. A. Lavrentiev, Sur la representation conforme des domains limites par des courbes rectifiables, Ann. Sci. École Norm. Sup. 54 (1937), 1-38.
  • [4] George Piranian, Two monotonic, singular, uniformly almost smooth functions, Duke Math. J. 33 (1966), 255–262. MR 0199320

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1989-0956000-1
Keywords: Inner functions, outer functions, Smirnov domains, harmonic measure, arc-length measure
Article copyright: © Copyright 1989 American Mathematical Society

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