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317,572
Harmonic Measure
 New Mathematical Monographs. Cambridge
, 2005
"... semantic web tools to integrate experimental ..."
Fine structure of harmonic measure
 St. Petersburg Math. J
, 1999
"... These notes are intended to review some results on the singularities of harmonic measure in the complex plane. Recall that the harmonic measure of a domain Ω is a family {ωa}a∈Ω of probability Borel measures on ∂Ω such that for a fixed set e,the function a ↦ → ωa(e) is ..."
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Cited by 32 (1 self)
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These notes are intended to review some results on the singularities of harmonic measure in the complex plane. Recall that the harmonic measure of a domain Ω is a family {ωa}a∈Ω of probability Borel measures on ∂Ω such that for a fixed set e,the function a ↦ → ωa(e) is
Harmonic measure and Uniform densities
 Indiana Univ. Math. J
"... Abstract. We study two problems concerning harmonic measure on “champagne subdomains ” of the unit disk D. These domains are obtained by removing from D little disks around sequences of points with a uniform distribution with respect to the pseudohyperbolic metric of D. We find (I) a necessary and s ..."
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Cited by 12 (1 self)
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Abstract. We study two problems concerning harmonic measure on “champagne subdomains ” of the unit disk D. These domains are obtained by removing from D little disks around sequences of points with a uniform distribution with respect to the pseudohyperbolic metric of D. We find (I) a necessary
SYMMETRIZATION AND HARMONIC MEASURE
"... Dedicated to Matti Vuorinen on the occasion of his sixtieth birthday. Abstract. We prove the equality statements for the classical symmetrization estimates for harmonic measure. In fact we prove more general results for αharmonic measure. The αharmonic measure is the hitting distribution of symme ..."
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Dedicated to Matti Vuorinen on the occasion of his sixtieth birthday. Abstract. We prove the equality statements for the classical symmetrization estimates for harmonic measure. In fact we prove more general results for αharmonic measure. The αharmonic measure is the hitting distribution
Harmonic measure and SLE
, 801
"... The motivation for this paper is twofold: to study multifractal spectrum of the harmonic measure and to better describe the geometry of Schramm’s SLE curves. The main result of this paper is the Theorem 2.2 in which we rigorously ..."
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Cited by 3 (0 self)
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The motivation for this paper is twofold: to study multifractal spectrum of the harmonic measure and to better describe the geometry of Schramm’s SLE curves. The main result of this paper is the Theorem 2.2 in which we rigorously
pHARMONIC MEASURE IS NOT SUBADDITIVE
"... Dedicated to the memory of Tom Wolff. Without his work this note would not have been possible. Abstract. When 1 < p < ∞ and p � = 2 the pharmonic measure on the boundary of the half plane R 2 + is not subadditive. In fact, there are finitely many sets E1, E2,...,Eκ on R, of pharmonic measure ..."
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Cited by 1 (0 self)
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Dedicated to the memory of Tom Wolff. Without his work this note would not have been possible. Abstract. When 1 < p < ∞ and p � = 2 the pharmonic measure on the boundary of the half plane R 2 + is not subadditive. In fact, there are finitely many sets E1, E2,...,Eκ on R, of pharmonic
Nonlinear harmonic measures on trees
 ANNALES ACADEMIÆ SCIENTIARUM FENNICÆ, VOLUMEN 28, 2003, 279{302
, 2003
"... We show that nonlinear harmonic measures on trees lack many desirable properties of set functions encountered in classical analysis. Let F be an averaging operator on R · and!F be the Fharmonic measure on a ·regular forward branching tree. Unless F is the usual average,!F is not a Choquet capacit ..."
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Cited by 5 (1 self)
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We show that nonlinear harmonic measures on trees lack many desirable properties of set functions encountered in classical analysis. Let F be an averaging operator on R · and!F be the Fharmonic measure on a ·regular forward branching tree. Unless F is the usual average,!F is not a Choquet
A NOTE ON HARMONIC MEASURE
"... Abstract. Let Ω be a subregion of {z: z  < 1} for which the Dirichlet problem is solvable, assume that 0 ∈ Ω and let ωΩ denote harmonic measure on ∂Ω for evaluation at 0. If E is a Borel subset of {z: z  = 1} and ωΩ(E)> 0, then we find a simply connected region G, where 0 ∈ G ⊆ {z: z  ..."
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Abstract. Let Ω be a subregion of {z: z  < 1} for which the Dirichlet problem is solvable, assume that 0 ∈ Ω and let ωΩ denote harmonic measure on ∂Ω for evaluation at 0. If E is a Borel subset of {z: z  = 1} and ωΩ(E)> 0, then we find a simply connected region G, where 0 ∈ G ⊆ {z: z
Convexity of limits of harmonic measures
, 2006
"... Preliminary version It is shown that, given a point x ∈ d, d ≥ 2, and open sets U1,...,Uk in d U containing x, any convex combination of the harmonic measures ε c n x for x with respect to Un, 1 ≤ n ≤ k, is the limit of a sequence (ε W c m x)m∈ of harmonic measures, where each Wm is an open subset o ..."
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Preliminary version It is shown that, given a point x ∈ d, d ≥ 2, and open sets U1,...,Uk in d U containing x, any convex combination of the harmonic measures ε c n x for x with respect to Un, 1 ≤ n ≤ k, is the limit of a sequence (ε W c m x)m∈ of harmonic measures, where each Wm is an open subset
Harmonic Measure, Infinite Kernels, and
, 1995
"... The vanishing of area for the infinite Nielsen kernel of an arbitrary open Riemann surface is shown to follow from iteration of a natural geometric operation on the unit disk. This operation compares the distribution of harmonic measure on the boundaries of two related simply connected domains, and ..."
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The vanishing of area for the infinite Nielsen kernel of an arbitrary open Riemann surface is shown to follow from iteration of a natural geometric operation on the unit disk. This operation compares the distribution of harmonic measure on the boundaries of two related simply connected domains
Results 1  10
of
317,572