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Martin points on open manifolds of non-positive curvature
Author(s):
Jianguo
Cao;
Huijun
Fan;
François
Ledrappier
Journal:
Trans. Amer. Math. Soc.
359
(2007),
5697-5723.
MSC (2000):
Primary 58J32;
Secondary 60J65
Posted:
July 3, 2007
MathSciNet review:
2336303
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Abstract:
The Martin boundary of a Cartan-Hadamard manifold describes a fine geometric structure at infinity, which is a sub-space of positive harmonic functions. We describe conditions which ensure that some points of the sphere at infinity belong to the Martin boundary as well. In the case of the universal cover of a compact manifold with Ballmann rank one, we show that Martin points are generic and of full harmonic measure. The result of this paper provides a partial answer to an open problem of S. T. Yau.
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Additional Information:
Jianguo
Cao
Affiliation:
Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556
Email:
jcao@nd.edu
Huijun
Fan
Affiliation:
School of Mathematical Sciences, Peking University, Beijing 100875, People's Republic of China
Email:
fanhj@math.pku.edu.cn
François
Ledrappier
Affiliation:
Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556
Email:
fledrapp@nd.edu
DOI:
10.1090/S0002-9947-07-04102-5
PII:
S 0002-9947(07)04102-5
Received by editor(s):
May 27, 2005
Posted:
July 3, 2007
Additional Notes:
The first author was supported in part by an NSF grant
The second author was partially supported by the Research Fund for returned overseas Chinese Scholars 20010107 and by the NSFC for Young Scholars 10401001
Copyright of article:
Copyright
2007,
American Mathematical Society
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