Harmonic Measure on Fractal Sets

  • D. Beliaev

    Royal Institute of Technology, Stockholm, Sweden
  • Stanislav Smirnov

    Université de Genève, Switzerland
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Many problems in complex analysis can be reduced to the evaluation of the universal spectrum: the supremum of multifractal spectra of harmonic measures for all planar domains. Its exact value is still unknown, with very few estimates available. We start with a brief survey of related problems and available estimates from above. Then we discuss in more detail estimates from below, describing the search for a fractal domain which attains the maximal possible spectrum.