@inbook{bce7717d2d064c4f85b36ea1ac6e6500,

title = "Asymptotic ratio of harmonic measures of sides of a boundary slit",

abstract = "Let l be a Jordan arc in the upper half-plane ℍ with the initial point at z = 0. For ζ ∈ l, let ω+(a, ζ) and ω−(a, ζ) denote the harmonic measures of the left and right shores of the slit lζ⊂ ℍ along the portion of the arc l travelled from 0 to ζ. In one of the seminars within the “Complex Analysis and Integrable Systems” semester held at the Mittag-Leffler Institute in 2011, D. Prokhorov suggested a study of the limit behavior of the quotient ω−(a, ζ)/ω+(a, ζ) as ζ → 0 along l. In recent publications, D. Prokhorov and his coauthors discussed this problem and proved several results for smooth slits. In this paper, we study the limit behavior of ω+(a, ζ)/ω−(a, ζ) for a broader class of continuous slits which includes radially and angularly oscillating slits. Some related questions concerning behavior of the driving term of the corresponding chordal L{\"o}wner equation are also discussed.",

keywords = "Boundary slits, Harmonic measure, L{\"o}wner equation",

author = "Alexander Solynin",

note = "Publisher Copyright: {\textcopyright} Springer International Publishing AG 2018. Copyright: Copyright 2018 Elsevier B.V., All rights reserved.",

year = "2018",

doi = "10.1007/978-3-319-70154-7_14",

language = "English",

series = "Trends in Mathematics",

publisher = "Springer International Publishing",

number = "9781493976584",

pages = "273--299",

booktitle = "Trends in Mathematics",

edition = "9781493976584",

}