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Bulletin of the American Mathematical Society
ISSN 1088-9485(e) ISSN 0273-0979(p)
     

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Book Information

Author(s): John B. Garnett and Donald E. Marshall
Title: Harmonic measure
Additional book information: Cambridge University Press, 2005, xv + 571, US$110, 0-521-47018-8


References:

[Bishop(1992)]
C. J. Bishop.
Some questions concerning harmonic measure.
In Partial Differential Equations with Minimal Smoothness and Applications (Chicago, IL, 1990), volume 42 of IMA Vol. Math. Appl., pages 89-97. Springer, New York, 1992. MR 1155854 (93f:30023)

[Bishop(2002)]
C. J. Bishop.
Quasiconformal Lipschitz maps, Sullivan's convex hull theorem and Brennan's conjecture.
Ark. Mat. 40(1):1-26, 2002. MR 1948883 (2003i:30063)

[Bishop et al.(1989)]
C. J. Bishop, L. Carleson, J. B. Garnett, and P. W. Jones.
Harmonic measures supported on curves.
Pacific J. Math. 138(2):233-236, 1989. MR 0996199 (90d:30069)

[Bishop and Jones(1990)]
C. J. Bishop and P. W. Jones.
Harmonic measure and arclength.
Ann. of Math. (2) 132(3):511-547, 1990. MR 1078268 (92c:30026)

[Bourgain(1987)]
J. Bourgain.
On the Hausdorff dimension of harmonic measure in higher dimension.
Invent. Math. 87(3):477-483, 1987. MR 0874032 (88b:31004)

[Carleson(1973)]
L. Carleson.
On the distortion of sets on a Jordan curve under conformal mapping.
Duke Math. J. 40:547-559, 1973. MR 0330430 (48:8767)

[Carleson(1985)]
L. Carleson.
On the support of harmonic measure for sets of Cantor type.
Ann. Acad. Sci. Fenn. Ser. A I Math. 10:113-123, 1985. MR 0802473 (87b:31002)

[Choi(2004)]
S. Choi.
The lower density conjecture for harmonic measure.
J. Anal. Math. 93:237-269, 2004. MR 2110330 (2005k:30049)

[Fernández et al.(1989)]
J. L. Fernández, J. Heinonen, and O. Martio.
Quasilines and conformal mappings.
J. Analyse Math. 52:117-132, 1989. MR 0981499 (90a:30017)

[Jones(1989)]
P. W. Jones.
Square functions, Cauchy integrals, analytic capacity, and harmonic measure.
In Harmonic Analysis and Partial Differential Equations (El Escorial, 1987), volume 1384 of Lecture Notes in Math., pages 24-68. Springer, Berlin, 1989. MR 1013815 (91b:42032)

[Jones and Wolff(1988)]
P. W. Jones and T. H. Wolff.
Hausdorff dimension of harmonic measures in the plane.
Acta Math. 161(1-2):131-144, 1988. MR 0962097 (90j:31001)

[Kaufman and Wu(1982)]
R. Kaufman and J. M. Wu.
Distortion of the boundary under conformal mapping.
Michigan Math. J. 29(3):267-280, 1982. MR 0674280 (84b:31003)

[Lavrent$ '$ev(1936)]
M. Lavrent$ '$ev.
Boundary problems in the theory of univalent functions.
Math. Sb. (N.S.) 43(1):815-846, 1936. MR 0155970 (27:5903)

[Lewis et al.(2005)]
J. L. Lewis, G. C. Verchota, and A. L. Vogel.
Wolff snowflakes.
Pacific J. Math. 218(1):139-166, 2005. MR 2224593

[Makarov(1985)]
N. G. Makarov.
On the distortion of boundary sets under conformal mappings.
Proc. London Math. Soc. (3) 51(2):369-384, 1985. MR 0794117 (87d:30012)

[McMillan(1969)]
J. E. McMillan.
Boundary behavior of a conformal mapping.
Acta Math. 123:43-67, 1969. MR 0257330 (41:1981)

[McMillan and Piranian(1973)]
J. E. McMillan and G. Piranian.
Compression and expansion of boundary sets.
Duke Math. J. 40:599-605, 1973. MR 0318492 (47:7039)

[Pommerenke(1986)]
C. Pommerenke.
On conformal mapping and linear measure.
J. Analyse Math. 46:231-238, 1986. MR 0861701 (88a:30055)

[Przytycki et al.(1989)]
F. Przytycki, M. Urbanski, and A. Zdunik.
Harmonic, Gibbs and Hausdorff measures on repellers for holomorphic maps. I.
Ann. of Math. (2) 130(1):1-40, 1989. MR 1005606 (91i:58115)

[Riesz and Riesz(1916)]
F. Riesz and M. Riesz.
Über die ranwerte einer analytischen Funcktionen.
Quartriéme Congress des Math. Scand., pages 27-44, 1916.

[Walden(1994)]
B. L. Walden.
$ L\sp p$-integrability of derivatives of Riemann mappings on Ahlfors-David regular curves.
J. Anal. Math. 63:231-253, 1994. MR 1269221 (94m:30022)

[Wolff(1993)]
T. H. Wolff.
Plane harmonic measures live on sets of $ \sigma$-finite length.
Ark. Mat. 31(1):137-172, 1993. MR 1230270 (94d:31002)

[Wolff(1995)]
T. H. Wolff.
Counterexamples with harmonic gradients in $ {\bf R}\sp 3$.
In Essays on Fourier Analysis in Honor of Elias M. Stein (Princeton, NJ, 1991), volume 42 of Princeton Math. Ser., pages 321-384. Princeton Univ. Press, Princeton, NJ, 1995. MR 1315554 (95m:31010)


Additional Information:

Reviewer(s):
Christopher J. Bishop
Affiliation: SUNY Stony Brook
Email: bishop@math.sunysb.edu

Review Information:
Journal: Bull. Amer. Math. Soc. 44 (2007), 267-276.

MSC (2000): Primary 30C85; Secondary 31A15
DOI: 10.1090/S0273-0979-06-01125-6
PII: S 0273-0979(06)01125-6
Posted: August 28, 2006
Copyright of article: Copyright 2006, American Mathematical Society


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