Hölder exponents of Green's functions of Cantor sets

DOI10.1007/BF03321678zbMath1151.31003MaRDI QIDQ934535

Jérémie Rostand, Thomas Ransford

Publication date: 29 July 2008

Published in: Computational Methods and Function Theory (Search for Journal in Brave)

zbMATH Keywords

capacityHölder continuity

Mathematics Subject Classification ID

General theory of numerical methods in complex analysis (potential theory, etc.) (65E05) Capacity and harmonic measure in the complex plane (30C85) Potentials and capacity, harmonic measure, extremal length and related notions in two dimensions (31A15)

Related Items (10)

Jackson's inequality in the complex plane and the Łojasiewicz-Siciak inequality of Green's function ⋮ On the best exponent in Markov inequality ⋮ On smoothness of the Green function for the complement of a rarefied Cantor-type set ⋮ Weakly equilibrium Cantor-type sets ⋮ Equivalence of the global and local Markov inequalities in the complex plane ⋮ Hölder continuity of the Green function and Markov brothers' inequality ⋮ Cantor polynomials and some related classes of OPRL ⋮ Hölder exponents of the Green functions of planar polynomial Julia sets ⋮ Hölder exponents for the pluricomplex Green function of Julia type sets ⋮ On the behaviour of constants in some polynomial inequalities

Cites Work

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• Complex dynamics
• The highest smoothness of the Green function implies the highest density of a set
• Iterated function systems, capacity and Green's functions
• On optimal smoothness of the Green function for the complement of a Cantor-type set
• Computation of capacity
• Markov's property of the Cantor ternary set
• Wiener's type regularity criteria on the complex plane
• Removable Singularities of Continuous Harmonic Functions in Rm.

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