Martin boundary points of a John domain and unions of convex sets

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 $\sqrt3$/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.

Journal

• Journal of the Mathematical Society of Japan

Journal of the Mathematical Society of Japan 58(1), 247-274, 2006-01-01

The Mathematical Society of Japan

Codes

• NII Article ID (NAID)
10017178462
• NII NACSIS-CAT ID (NCID)
AA0070177X
• Text Lang
ENG
• Article Type
Journal Article
• ISSN
00255645
• NDL Article ID
7783405
• NDL Source Classification
ZM31(科学技術--数学)
• NDL Call No.
Z53-A209
• Data Source
CJP  CJPref  NDL  J-STAGE

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