Conformal Invariants in Simply Connected Domains

Effective Conformal Transformation of Smooth, Simply Connected Domains.

1. Statement of Problem.-Many problems in plane potential theory can be solved easily, if one knows how to map the interior (or exterior) of a given closed curve C in the z-plane, conformally and one-one onto the interior (or exterior) of the unit circle t = e"' in the t-plane. This can be done by tabulated functions in some cases, but even in such cases, the solution often involves one or more...

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Donaldson invariants for non-simply connected manifolds

We study Coulomb branch (“u-plane”) integrals for N = 2 supersymmetric SU(2), SO(3) Yang-Mills theory on 4-manifolds X of b1(X) > 0, b + 2 (X) = 1. Using wall-crossing arguments we derive expressions for the Donaldson invariants for manifolds with b1(X) > 0, b+2 (X) > 0. Explicit expressions for X = CP 1 × Fg, where Fg is a Riemann surface of genus g are obtained using Kronecker’s double series...

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Harmonic Measure in Simply Connected Domains

Let Ω be a bounded simply connected domain in the complex plane, C. Let N be a neighborhood of ∂Ω, let p be fixed, 1 < p < ∞, and let û be a positive weak solution to the p Laplace equation in Ω ∩N. Assume that û has zero boundary values on ∂Ω in the Sobolev sense and extend û to N \ Ω by putting û ≡ 0 on N \ Ω. Then there exists a positive finite Borel measure μ̂ on C with support contained in ...

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Harmonic Measure in Simply Connected Domains Revisited

Let Ω be a bounded simply connected domain in the complex plane, C. Let N be a neighborhood of ∂Ω, let p be fixed, 1 < p < ∞, and let û be a positive weak solution to the p Laplace equation in Ω ∩N. Assume that û has zero boundary values on ∂Ω in the Sobolev sense and extend û to N \ Ω by putting û ≡ 0 on N \ Ω. Then there exists a positive finite Borel measure μ̂ on C with support contained in ...

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p Harmonic Measure in Simply Connected Domains

Let Ω be a bounded simply connected domain in the complex plane, C. Let N be a neighborhood of ∂Ω, let p be fixed, 1 < p < ∞, and let û be a positive weak solution to the p Laplace equation in Ω ∩N. Assume that û has zero boundary values on ∂Ω in the Sobolev sense and extend û to N \ Ω by putting û ≡ 0 on N \ Ω. Then there exists a positive finite Borel measure μ̂ on C with support contained in ...

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Conformal Invariants in Simply Connected Domains

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منابع مشابه

Effective Conformal Transformation of Smooth, Simply Connected Domains.

Donaldson invariants for non-simply connected manifolds

Harmonic Measure in Simply Connected Domains

Harmonic Measure in Simply Connected Domains Revisited

p Harmonic Measure in Simply Connected Domains

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