Remote Access Conformal Geometry and Dynamics
Green Open Access

Conformal Geometry and Dynamics

ISSN 1088-4173

 
 

 

A note on the harmonic measure doubling condition


Authors: Ole J. Broch, Kari Hag and Steffen Junge
Journal: Conform. Geom. Dyn. 15 (2011), 1-6
MSC (2010): Primary 30C85, 30C62
DOI: https://doi.org/10.1090/S1088-4173-2010-00222-5
Published electronically: January 24, 2011
MathSciNet review: 2769220
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We present a detailed and self-contained proof of the harmonic measure doubling characterization of bounded quasidisks due to Jerison and Kenig.


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

  • 1. L. V. Ahlfors. Lectures on Quasiconformal Mappings. 2nd ed. University Lecture Series, Amer. Math. Soc., 2005. MR 2241787 (2009d:30001)
  • 2. J. B. Garnett and D. E. Marshall. Harmonic Measure. New Mathematical Monographs 2, Cambridge, 2005. MR 2150803 (2006g:31002)
  • 3. F. W. Gehring. Characteristic properties of quasidisks. Les presses de l'Université de Montréal, 1982. MR 674294 (84a:30036)
  • 4. F. W. Gehring and K. Hag. Sewing homeomorphisms and quasidisks. Comput. Methods. Funct. Theory 3 (2003), 143-150. MR 2082011 (2005e:30033)
  • 5. K. Hag. What is a disk? Banach Center Publications. 48 (1999), 43-53. MR 1709973 (2001d:30025)
  • 6. D. S. Jerison and C. E. Kenig. Boundary Behaviour of Harmonic Functions in Non-tangentially Accessible Domains. Adv. Math. 46 (1982), 80-147. MR 676988 (84d:31005b)
  • 7. K. Kim and N. Langmeyer. Harmonic measure and hyperbolic distance in John disks. Math. Scand. 83 (1998), 283-299. MR 1673938 (2000a:30038)
  • 8. J. Krzyz. Quasicircles and harmonic measure. Ann. Acad. Sci Fenn. (Ser. A. I. Math.) 12 (1987), 19-24. MR 877575 (88f:30033)

Similar Articles

Retrieve articles in Conformal Geometry and Dynamics of the American Mathematical Society with MSC (2010): 30C85, 30C62

Retrieve articles in all journals with MSC (2010): 30C85, 30C62


Additional Information

Ole J. Broch
Affiliation: SINTEF Fisheries and aquaculture, NO 7465 Trondheim, Norway
Email: ole.jacob.broch@sintef.no

Kari Hag
Affiliation: Department of Mathematical Sciences, Norwegian University of Science and Technology, NO 7491 Trondheim, Norway
Email: kari@math.ntnu.no

Steffen Junge
Affiliation: Department of Mathematical Sciences, Norwegian University of Science and Technology, NO 7491 Trondheim, Norway
Email: steffen.junge@math.ntnu.no

DOI: https://doi.org/10.1090/S1088-4173-2010-00222-5
Keywords: Harmonic measure, quasidisk
Received by editor(s): August 9, 2010
Published electronically: January 24, 2011
Article copyright: © Copyright 2010 American Mathematical Society

American Mathematical Society