Martin boundary points of a John domain and unions of convex sets
Journal article, 2006
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 $\sqrt3/2$ , 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.
convex set
tract
John domain
Carleson estimate
quasihyperbolic metric
weak boundary Harnack principle
Martin boundary
Domar's theorem
Author
Hiroaki Aikawa
Kentaro Hirata
Torbjörn Lundh
University of Gothenburg
Chalmers, Mathematical Sciences, Mathematics
Journal of the Mathematical Society of Japan
0025-5645 (ISSN) 18811167 (eISSN)
Vol. 58 1 247-274Subject Categories
Mathematical Analysis