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Book Review
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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)]
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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)]
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Harmonic measures supported on curves. Pacific J. Math. 138(2):233-236, 1989. MR 0996199 (90d:30069) - [Bishop and Jones(1990)]
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Harmonic measure and arclength. Ann. of Math. (2) 132(3):511-547, 1990. MR 1078268 (92c:30026) - [Bourgain(1987)]
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On the Hausdorff dimension of harmonic measure in higher dimension. Invent. Math. 87(3):477-483, 1987. MR 0874032 (88b:31004) - [Carleson(1973)]
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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)]
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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.
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- 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)]
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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)]
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-integrability of derivatives of Riemann mappings on Ahlfors-David regular curves. J. Anal. Math. 63:231-253, 1994. MR 1269221 (94m:30022) - [Wolff(1993)]
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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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