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Algebra i Analiz, 1998, Volume 10, Issue 2, Pages 1–62 (Mi aa980)  

This article is cited in 70 scientific papers (total in 70 papers)

Expository Surveys

Fine structure of harmonic measure

N. G. Makarov

Department of Mathematics, Caltech, Pasadena, CA

Keywords: Harmonic measure, fractals, conformal map, universal spectrum.

Full text: PDF file (2135 kB)

English version:
St. Petersburg Mathematical Journal, 1999, 10:2, 217–268

Bibliographic databases:

Received: 05.04.1997
Language:

Citation: N. G. Makarov, “Fine structure of harmonic measure”, Algebra i Analiz, 10:2 (1998), 1–62; St. Petersburg Math. J., 10:2 (1999), 217–268

Citation in format AMSBIB
\Bibitem{Mak98}
\by N.~G.~Makarov
\paper Fine structure of harmonic measure
\jour Algebra i Analiz
\yr 1998
\vol 10
\issue 2
\pages 1--62
\mathnet{http://mi.mathnet.ru/aa980}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1629379}
\zmath{https://zbmath.org/?q=an:0909.30016}
\transl
\jour St. Petersburg Math. J.
\yr 1999
\vol 10
\issue 2
\pages 217--268


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    This publication is cited in the following articles:
    1. Makarov N., Smirnov S., “On “thermodynamics” of rational maps I. Negative spectrum”, Communications in Mathematical Physics, 211:3 (2000), 705–743  crossref  mathscinet  zmath  adsnasa  isi  scopus
    2. Kayumov I.R., “The integral means spectrum for lacunary series”, Ann. Acad. Sci. Fenn. Math., 26:2 (2001), 447–453  mathscinet  zmath  isi
    3. Hedenmalm H., “The dual of a Bergman space on simply connected domains”, J. Anal. Math., 88 (2002), 311–335  crossref  mathscinet  zmath  isi  scopus
    4. Kayumov I.R., “The law of the iterated logarithm for locally univalent functions”, Ann. Acad. Sci. Fenn. Math., 27:2 (2002), 357–364  mathscinet  zmath  isi
    5. Beliaev D.B., Smirnov S.K., “On dimension of porous measures”, Math. Ann., 323:1 (2002), 123–141  crossref  mathscinet  zmath  isi  scopus
    6. Bishop Ch.J., “Quasiconformal Lipschitz maps, Sullivan's convex hull theorem and Brennan's conjecture”, Ark. Mat., 40:1 (2002), 1–26  crossref  mathscinet  zmath  adsnasa  isi  scopus
    7. Binder I., Makarov N., Smirnov S., “Harmonic measure and polynomial Julia sets”, Duke Math. J., 117:2 (2003), 343–365  crossref  mathscinet  zmath  isi  scopus
    8. I. R. Kayumov, “Sharp Estimates for Integral Means for Three Classes of Domains”, Math. Notes, 76:4 (2004), 472–477  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    9. Rohde S., Zinsmeister M., “Variation of the conformal radius”, J. Anal. Math., 92 (2004), 105–115  crossref  mathscinet  zmath  isi  scopus
    10. Przytycki F., Rivera-Letelier J., Smirnov S., “Equality of pressures for rational functions”, Ergodic Theory Dynam. Systems, 24:3 (2004), 891–914  crossref  mathscinet  zmath  isi  scopus
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    12. Kesseböhmer M., Stratmann B.O., “A multifractal formalism for growth rates and applications to geometrically finite Kleinian groups”, Ergodic Theory Dynam. Systems, 24:1 (2004), 141–170  crossref  mathscinet  zmath  isi
    13. I. R. Kayumov, “Spectrum of integral means and the modified Bessel function of zero order”, St. Petersburg Math. J., 17:3 (2006), 453–463  mathnet  crossref  mathscinet  zmath
    14. Hedenmalm H., Shimorin S., “Weighted Bergman spaces and the integral means spectrum of conformal mappings”, Duke Math. J., 127:2 (2005), 341–393  crossref  mathscinet  zmath  isi  scopus
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    17. Grebenkov D.S., Lebedev A.A., Filoche M., Sapoval B., “Multifractal properties of the harmonic measure on Koch boundaries in two and three dimensions”, Phys. Rev. E (3), 71:5 (2005), 056121, 11 pp.  crossref  mathscinet  adsnasa  isi  scopus
    18. Rohde S., Schramm O., “Basic properties of SLE”, Annals of Mathematics, 161:2 (2005), 883–924  crossref  mathscinet  zmath  isi  scopus
    19. Beliaev D., Smirnov S., “Harmonic measure on fractal sets”, European Congress of Mathematics, 2005, 41–59  mathscinet  zmath  isi
    20. Batakis A., “Dimension of the harmonic measure of non-homogeneous Cantor sets”, Ann. Inst. Fourier (Grenoble), 56:6 (2006), 1617–1631  crossref  mathscinet  zmath  isi  scopus
    21. Gruzberg I.A., “Stochastic geometry of critical curves, Schramm-Loewner evolutions and conformal field theory”, J. Phys. A, 39:41 (2006), 12601–12655  crossref  mathscinet  zmath  adsnasa  isi  scopus
    22. Kayumov I.R., “Lower estimates for integral means of univalent functions”, Ark. Mat., 44:1 (2006), 104–110  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    23. I. R. Kayumov, “Granichnoe povedenie analiticheskikh proizvedenii Rissa v kruge”, Matem. tr., 9:1 (2006), 34–51  mathnet  mathscinet  elib
    24. I. R. Kayumov, “Spektr integralnykh srednikh i zakon povtornogo logarifma dlya konformnykh otobrazhenii”, Uchen. zap. Kazan. gos. un-ta. Ser. Fiz.-matem. nauki, 148, no. 2, Izd-vo Kazanskogo un-ta, Kazan, 2006, 85–96  mathnet  zmath
    25. Heurteaux Y., “Dimension of measures: The probabilistic approach”, Publ. Mat., 51:2 (2007), 243–290  crossref  mathscinet  zmath  isi  scopus
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    27. I. R. Kayumov, “On an Inequality for the Universal Spectrum of Integral Means”, Math. Notes, 84:1 (2008), 137–141  mathnet  crossref  crossref  mathscinet  isi
    28. Baranov A., Hedenmalm H., “Boundary properties of Green functions in the plane”, Duke Math. J., 145:1 (2008), 1–24  crossref  mathscinet  zmath  isi  elib  scopus
    29. Beliaev D., “Integral means spectrum of random conformal snowflakes”, Nonlinearity, 21:7 (2008), 1435–1442  crossref  mathscinet  zmath  adsnasa  isi  scopus
    30. Monreal Galán N., “The dyadic integral means spectrum for Bloch functions”, Bull. Lond. Math. Soc., 40:2 (2008), 319–326  crossref  mathscinet  zmath  isi  scopus
    31. Beliaev D., Smirnov S., “Harmonic Measure and SLE”, Comm. Math. Phys., 290:2 (2009), 577–595  crossref  mathscinet  zmath  adsnasa  isi  scopus
    32. Binder I., “Phase transition for the universal bounds on the integral means spectrum”, Nonlinearity, 22:8 (2009), 1857–1867  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    33. Beliaev D., Smirnov S., “Random conformal snowflakes”, Annals of Mathematics, 172:1 (2010), 597–615  crossref  mathscinet  zmath  isi
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    35. Simon B., “Fine Structure of the Zeros of Orthogonal Polynomials: A Progress Report”, Recent Trends in Orthogonal Polynomials and Approximation Theory, Contemporary Mathematics, 507, 2010, 241–254  crossref  mathscinet  zmath  isi
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