Geometric theorems and problems for harmonic measure
type: Item
instance of: scholarly article
title: Geometric theorems and problems for harmonic measure
zbMATH Open document ID: 1006.31002
author: Dimitrios Betsakos
published in: Rocky Mountain Journal of Mathematics
publication date: 2002-05-22T00:00:00Z
full work available at URL: CONT31-3.html
review text: The author provides a wide-ranging review of results and open problems for harmonic measure that have simple geometric characters. These include classical projection estimates of Beurling, Nevanlinna and Hall, and recent results of Marshall, Sundberg, Solynin and others. The paper provides an interesting compendium of the current situation in various areas, and is recommended reading for those interested in harmonic measure in the plane.
Mathematics Subject Classification ID: 31A15
Mathematics Subject Classification ID: 30C85
zbMATH DE Number: 1744053
zbMATH Keywords: harmonic measure
zbMATH Keywords: symmetrisation
zbMATH Keywords: polarisation
zbMATH Keywords: review of results and open problems
reviewed by: David A. Brannan
MaRDI profile type: Publication
OpenAlex ID: W2087696923
cites work: A conformal mapping technique for infinitely connected regions
cites work: Integral means, univalent functions and circular symmetrization
cites work: Q3876182
cites work: Q3954045
cites work: Q3027325
cites work: On the harmonic measure of slit domains
cites work: Ahlfors and conformal invariants
cites work: An extremal problem for certain subharmonic functions in the plane
cites work: Q4312128
cites work: Spherical rearrangements, subharmonic functions, and \(\ast\)-functions in \(n\)-space
cites work: Research Problems in Complex Analysis
cites work: On certain harmonic measures on the unit disk
cites work: Q4400428
cites work: Q4270238
cites work: Harmonic measure on simply connected domains of fixed inradius
cites work: Extensions of beurling's shove theorem for harmonic measure
cites work: The collected works of Arne Beurling. Volume 1: Complex analysis. Volume 2: Harmonic analysis. Ed. by Lennart Carleson, Paul Malliavin, John Neuberger, John Wermer
cites work: Q5287472
cites work: How geodesics approach the boundary in a simply connected domain
cites work: An approach to symmetrization via polarization
cites work: Q3961718
cites work: ON THE CHANGE IN HARMONIC MEASURE UNDER SYMMETRIZATION
cites work: Symmetrization in the geometric theory of functions of a complex variable
cites work: On analytic functions which are in \(H^ p\) for some positive p
cites work: On beurling's theorem for harmonic measure and the rings of saturn
cites work: On some questions of uniqueness in the theory of symmetrization
cites work: Quasilines and conformal mappings
cites work: Estimates of the Harmonic Measure of a Continuum in the Unit Disk
cites work: Q3475543
cites work: A Note on Hall's Lemma
cites work: Q3760830
cites work: Q5574105
cites work: Estimates of harmonic measures
cites work: On an extremal configuration for capacity
cites work: Q5765885
cites work: Q3250731
cites work: On a theorem of Tord Hall
cites work: Q4692700
cites work: Q3852455
cites work: On the coefficients and means of functions omitting values
cites work: Longueurs extrémales et théorie des fonctions
cites work: On the existence of certain general extremal metrics
cites work: On the Denjoy Conjecture
cites work: Q4052450
cites work: Some Estimates for Harmonic Measures. II
cites work: Q4673520
cites work: Moduli of families of curves and quadratic differentials
cites work: Extremal problems involving logarithmic and Green capacity
cites work: Harmonic Measure and Radial Projection
cites work: Harmonic measure of curves in the disk
cites work: Q4752728
cites work: Q5760574
cites work: Projection estimates for harmonic measure
cites work: The Hayman-Wu Constant
cites work: Q4000499
cites work: Q3048019
cites work: A remark on non-existence of an algebra norm for the algebra of continuous functions on a topological space admitting an unbounded continuous function
cites work: Steiner symmetry, horizontal convexity and some Dirichlet problems
cites work: Martin Boundaries of Denjoy Domains
cites work: Q3364823
cites work: Q3127994

Geometric theorems and problems for harmonic measure (cites work)
cites work: Extremal problems on conformal moduli and estimates for harmonic measures

Geometric theorems and problems for harmonic measure (cites work)
cites work: Harmonic measure of radial line segments and symmetrization

Geometric theorems and problems for harmonic measure (cites work)
cites work: Q3259806

Geometric theorems and problems for harmonic measure (cites work)
cites work: Properties of Conformal Invariants

Geometric theorems and problems for harmonic measure (cites work)
cites work: Q3781355

Geometric theorems and problems for harmonic measure (DOI)
DOI: 10.1216/RMJM/1020171668