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Volume growth and parabolicity
Author(s):
Ilkka
Holopainen;
Pekka
Koskela
Journal:
Proc. Amer. Math. Soc.
129
(2001),
3425-3435.
MSC (2000):
Primary 58J60, 53C20, 31C12
Posted:
April 24, 2001
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Abstract:
We characterize  -parabolicity of a noncompact complete Riemannian manifold  in terms of the volume growth of  under very weak assumptions on  . Some of the results also apply to the setting of metric measure spaces.
References:
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Additional Information:
Ilkka
Holopainen
Affiliation:
Department of Mathematics, University of Helsinki, P.O. Box 4 (Yliopistonkatu 5), FIN-00014 Helsinki, Finland
Email:
ilkka.holopainen@helsinki.fi
Pekka
Koskela
Affiliation:
Department of Mathematics, University of Jyväskylä, P.O. Box 35, FIN-40351 Jyväskylä, Finland
Email:
pkoskela@math.jyu.fi
DOI:
10.1090/S0002-9939-01-05954-8
PII:
S 0002-9939(01)05954-8
Keywords:
Volume growth,
harmonic function,
Green's function,
parabolicity
Received by editor(s):
December 1, 1999
Received by editor(s) in revised form:
April 3, 2000
Posted:
April 24, 2001
Additional Notes:
The first author's work was supported by the Academy of Finland, projects 6355 and 44333
The second author's work was supported by the Academy of Finland, project 39788
Communicated by:
Albert Baernstein II
Copyright of article:
Copyright
2001,
American Mathematical Society
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