Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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?)

  • [1] P. L. Duren, Theory of $ {H^p}$ space, Academic Press, New York, 1970. MR 0268655 (42:3552)
  • [2] P. L. Duren, H. S. Shapiro and A. L. Shields, Singular measures and domains not of Smirnov type, Duke Math. J. 33 (1966), 247-254. MR 0199359 (33:7506)
  • [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] G. Piranian, Two monotonic, singular uniformly almost smooth functions, Duke Math. J. 33 (1966), 255-262. MR 0199320 (33:7468)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 30C35, 30C85, 30D55, 31A15

Retrieve articles in all journals with MSC: 30C35, 30C85, 30D55, 31A15


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

American Mathematical Society