Acta Mathematica

Hausdorff dimension of harmonic measures in the plane

Peter W. Jones and Thomas H. Wolff

Full-text: Open access

Article information

Source
Acta Math. Volume 161 (1988), 131-144.

Dates
Received: 3 September 1986
Revised: 14 March 1988
First available in Project Euclid: 31 January 2017

Permanent link to this document
http://projecteuclid.org/euclid.acta/1485890540

Digital Object Identifier
doi:10.1007/BF02392296

Zentralblatt MATH identifier
0667.30020

Rights
1988 © Almqvist & Wiksell

Citation

Jones, Peter W.; Wolff, Thomas H. Hausdorff dimension of harmonic measures in the plane. Acta Math. 161 (1988), 131--144. doi:10.1007/BF02392296. http://projecteuclid.org/euclid.acta/1485890540.


Export citation

References

  • [Anc] Ancona, A., Negative curvature, elliptic operators, and the Martin boundary. Ann. of Math., 125 (1987), 495–536.
  • [B] Bourgain, J., On the Hausdorff dimension of harmonic measure in higher dimensions. To appear in Invent. Math.
  • [B-C] Brossard, J. & Carmona, R., Can one hear the dimension of a fractal?Comm. Math. Phys., 104 (1986), 103–122.
  • [C1] Carleson, L., Selected problems on exceptional sets. Wadsworth, 1983.
  • [C2] —, On the support of harmonic measure for sets of Cantor type. Ann. Acad. Sci. Fenn., 10 (1985), 113–123.
  • [J-M] Jones, P. W. & Marshall, D. E., Critical points of Green’s function, harmonic measure, and the corona problem. Ark. Mat., 23 (1985), 281–314.
  • [K-W] Kaufman, R. & Wu, J. M., On the snowflake domain. Ark. Mat., 23 (1985), 177–183.
  • [Mak1] Makarov, N. G., Distortion of boundary sets under conformal mappings. Proc. London Math. Soc. (3), 51 (1985), 369–384.
  • [Mak2] Makarov, N. G., Conformal mapping and Hausdorff measure. Preprint 1985.
  • [Man] Manning, A., The dimension of the maximal measure for a polynomial map. Ann. of Math., 119 (1984), 425–430.
  • [Ø1] Øksendal, B., Null sets for measures orthogonal to R(X). Amer. J. Math., 94 (1972), 331–342.
  • [Ø2] —, Brownian motion and sets of harmonic measure zero. Pacific J. Math., 95 (1981), 179–192
  • [Po] Pommerenke, Ch., On conformal mapping and linear measure. Preprint 1985.
  • [Pr] Przytycki, F., Hausdorff dimension of harmonic measure on the boundary of an attractive basin for a homomorphic map. Invent. Math., 80 (1985), 161–179.