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

• 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.

Subject headings

NATURVETENSKAP  -- Matematik -- Matematisk analys (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Mathematical Analysis (hsv//eng)

Keyword

John domain

convex set

Martin boundary

quasihyperbolic metric

Carleson estimate

Domar's theorem

tract

weak boundary Harnack principle

convex set

Publication and Content Type

ref (subject category)

art (subject category)