Minimal Kernels, Quadrature Identities and Proportional Harmonic Measures

Akeroyd, John R.; Karber, Kristi; Solynin, Alexander Yu.

doi:10.1216/rmjm/1181069346

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Acknowledgements1

A Reflection Principle For Harmonic Measure1

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2014

2015

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Cited by 2 publications

(2 citation statements)

References 8 publications

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“…The authors thank Malik Younsi for interesting discussions on the subject, for posing Question 1.1 and for pointing out inequality (1.2) and the article [2]. Also, the authors thank Alexey Lukashov for pointing out the article [7], and the referee for drawing their attention to the references [1,6,13,17].…”

Section: Acknowledgementsmentioning

confidence: 91%

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On the Harmonic Measure and Capacity of Rational Lemniscates

Pouliasis

Ransford

2015

Potential Anal

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Section: Acknowledgementsmentioning

confidence: 91%

“…Remark. Theorem 3.1 is a close relative of problems on the proportionality of harmonic measures studied in [1] and [17].…”

Section: A Reflection Principle For Harmonic Measurementioning

confidence: 92%

On the Harmonic Measure and Capacity of Rational Lemniscates

Pouliasis

Ransford

2015

Potential Anal

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Intrinsic circle domains

Crane

2014

Conform. Geom. Dyn.

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Using quasiconformal mappings, we prove that any Riemann surface of finite connectivity and finite genus is conformally equivalent to an intrinsic circle domain Ω in a compact Riemann surface S. This means that each connected component B of S \ Ω is either a point or a closed geometric disc with respect to the complete constant curvature conformal metric of the Riemann surface (Ω ∪ B). Moreover the pair (Ω, S) is unique up to conformal isomorphisms. We give a generalization to countably infinite connectivity. Finally we show how one can compute numerical approximations to intrinsic circle domains using circle packings and conformal welding.

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Minimal Kernels, Quadrature Identities and Proportional Harmonic Measures

Cited by 2 publications

References 8 publications

On the Harmonic Measure and Capacity of Rational Lemniscates

On the Harmonic Measure and Capacity of Rational Lemniscates

Intrinsic circle domains

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