منابع مشابه
Rigidity of harmonic measure
Let J be the Julia set of a conformal dynamics f . Provided that f is polynomial-like we prove that the harmonic measure on J is mutually absolutely continuous with the measure of maximal entropy if and only if f is conformally equivalent to a polynomial. This is no longer true for generalized polynomial-like maps. But for such dynamics the coincidence of classes of these two measures turns out...
متن کاملFine Structure of Harmonic Measure
We would like to know how harmonic measure is distributed over the the boundary. Typically, the concentration of harmonic measure varies widely — it is higher on the more ”exposed” parts of the boundary and smaller on the ”screened” parts. It has become usual (see, e.g., [H]) to consider the dimension spectrum of a measure — a continuum of parameters characterising the size of the sets where th...
متن کاملHarmonic Measure in Convex Domains
Introduction. Let Q be an open, convex subset of R^. At almost every point x of dQ, with respect to surface measure da, there is a unique outer unit normal 6. The map g: dQ -* S given by g(x) = 9 and defined almost everywhere is called the Gauss map. (S, n = N 1, is the unit sphere in R^.) Suppose that the origin 0 belongs to Q. Harmonic measure for fit at 0 is the probability measure co such t...
متن کاملHarmonic Measure and Some Removability Problems
We deal with some applications of Marcinkiewicz integrals to problems related to harmonic measure on the one hand, and to removability problems for Sobolev spaces and quasiconformal mappings on the other hand. Techniques of this type have been used by Carleson, Jones, Makarov, Smirnov... to address these problems, and as a general program to understand harmonic functions on complicated domains ...
متن کاملHarmonic Measure and Estimates of Green's Function
The study of exceptional sets for nontangential limits of harmonic functions has led to the problem of the equivalence of harmonic measure and surface measure on the boundary of Lipschitz domains. In this note we will review the development of these results. We will see how estimates of Green's function can be used to relate the measures and look at methods of obtaining the desired estimates. I...
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ژورنال
عنوان ژورنال: Michigan Mathematical Journal
سال: 1972
ISSN: 0026-2285
DOI: 10.1307/mmj/1029000900