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JANUARY, 2006 Martin boundary points of a John domain and unions of convex sets
Hiroaki AIKAWA, Kentaro HIRATA, Torbjörn LUNDH
J. Math. Soc. Japan 58(1): 247-274 (JANUARY, 2006). DOI: 10.2969/jmsj/1145287101

Abstract

We show that a John domain has finitely many minimal Martin boundary points at each Euclidean boundary point. The number of minimal Martin boundary points is estimated in terms of the John constant. In particular, if the John constant is bigger than 3 / 2 , then there are at most two minimal Martin boundary points at each Euclidean boundary point. For a class of John domains represented as the union of convex sets we give a sufficient condition for the Martin boundary and the Euclidean boundary to coincide.

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Hiroaki AIKAWA. Kentaro HIRATA. Torbjörn LUNDH. "Martin boundary points of a John domain and unions of convex sets." J. Math. Soc. Japan 58 (1) 247 - 274, JANUARY, 2006. https://doi.org/10.2969/jmsj/1145287101

Information

Published: JANUARY, 2006
First available in Project Euclid: 17 April 2006

zbMATH: 1092.31006
MathSciNet: MR2204573
Digital Object Identifier: 10.2969/jmsj/1145287101

Subjects:
Primary: 31B05 , 31B25 , 31C35

Keywords: Carleson estimate , convex set , Domar's theorem , John domain , Martin boundary , quasihyperbolic metric , tract , weak boundary Harnack principle

Rights: Copyright © 2006 Mathematical Society of Japan

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Vol.58 • No. 1 • JANUARY, 2006
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