Volume growth and parabolicity

Authors:
Ilkka Holopainen and Pekka Koskela

Journal:
Proc. Amer. Math. Soc. **129** (2001), 3425-3435

MSC (2000):
Primary 58J60, 53C20, 31C12

DOI:
https://doi.org/10.1090/S0002-9939-01-05954-8

Published electronically:
April 24, 2001

MathSciNet review:
1845022

Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.

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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:
https://doi.org/10.1090/S0002-9939-01-05954-8

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

Published electronically:
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

Article copyright:
© Copyright 2001
American Mathematical Society