On the harmonic measure and capacity of rational lemniscates

DOI10.1007/s11118-015-9508-zzbMath1350.30041arXiv1510.08124OpenAlexW1840589071MaRDI QIDQ259208

Stamatis Pouliasis, Thomas Ransford

Publication date: 11 March 2016

Published in: Potential Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1510.08124

zbMATH Keywords

capacityrational functionsharmonic measurelemniscatesLindelöf principle

Mathematics Subject Classification ID

Maximum principle, Schwarz's lemma, Lindelöf principle, analogues and generalizations; subordination (30C80) Capacity and harmonic measure in the complex plane (30C85) Polynomials and rational functions of one complex variable (30C10) Potentials and capacity, harmonic measure, extremal length and related notions in two dimensions (31A15)

Related Items (2)

On the geometry of random lemniscates ⋮ A refinement for rational functions of Pólya's method to construct Voronoi diagrams

Cites Work

• Analytic capacity, the Cauchy transform, and non-homogeneous Calderón-Zygmund theory
• Some inequalities for polynomials and rational functions associated with lemniscates
• Majorization principles for meromorphic functions
• Area and the inradius of lemniscates
• Lindelöf's principle and estimates for holomorphic functions involving area, diameter or integral means
• Rational Ahlfors functions
• Minimal kernels, quadrature identities and proportional harmonic measures
• Cauchy transforms of point masses: the logarithmic derivative of polynomials
• On the Lindelöf principle
• Shapes, fingerprints and rational lemniscates
• Quadratic Differentials and Weighted Graphs on Compact Surfaces
• Two-dimensional shapes and lemniscates
• Area, capacity and diameter versions of Schwarz’s Lemma
• Symmetrization in the geometric theory of functions of a complex variable
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