The Martin Boundary in the Parabolic Context

1984 ◽  
pp. 363-383
Author(s):  
J. L. Doob
Keyword(s):  
Martin Boundary

Martin boundary of unlimited covering surfaces

2000 ◽  
Vol 82 (1) ◽  
pp. 55-72 ◽  
Author(s):  
Hiroaki Masaoka ◽  
Shigeo Segawa
Keyword(s):  
Martin Boundary

Martin boundary of a plane domain, whose complement is situated on the line

1990 ◽  
Vol 47 (2) ◽  
pp. 121-128
Author(s):  
P. P. Kargaev
Keyword(s):  
Martin Boundary ◽  
Plane Domain

scholarly journals Martin boundary of a killed random walk on a quadrant

2010 ◽  
Vol 38 (3) ◽  
pp. 1106-1142 ◽  
Author(s):  
Irina Ignatiouk-Robert ◽  
Christophe Loree
Keyword(s):  
Random Walk ◽  
Martin Boundary

scholarly journals The asymptotic Dirichlet problems on manifolds with unbounded negative curvature

2018 ◽  
Vol 167 (01) ◽  
pp. 133-157
Author(s):  
RAN JI
Keyword(s):  
Dirichlet Problem ◽  
Negative Curvature ◽  
Probabilistic Method ◽  
Martin Boundary ◽  
Dirichlet Problems ◽  
Curvature Condition ◽  
New Approach ◽  
Harnack Inequalities ◽  
Geometric Boundary ◽  
Analytical Proof

AbstractElton P. Hsu used probabilistic method to show that the asymptotic Dirichlet problem is uniquely solvable under the curvature condition −Ce(2−η)r(x) ≤ KM(x) ≤ −1 with η > 0. We give an analytical proof of the same statement. In addition, using this new approach we are able to establish two boundary Harnack inequalities under the curvature condition −Ce(2/3−η)r(x) ≤ KM(x) ≤ −1 with η > 0. This implies that there is a natural homeomorphism between the Martin boundary and the geometric boundary of M. As far as we know, this is the first result of this kind under unbounded curvature conditions. Our proof is a modification of an argument due to M. T. Anderson and R. Schoen.

Regular Points of the Martin Boundary

1970 ◽  
Vol 15 (4) ◽  
pp. 619-629
Author(s):  
M. G. Shur
Keyword(s):  
Martin Boundary
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