## Volume growth and parabolicity

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- by Ilkka Holopainen and Pekka Koskela PDF
- Proc. Amer. Math. Soc.
**129**(2001), 3425-3435 Request permission

## Abstract:

We characterize $p$-parabolicity of a noncompact complete Riemannian manifold $M$ in terms of the volume growth of $M$ under very weak assumptions on $M$. 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
- MR Author ID: 290418
- Email: ilkka.holopainen@helsinki.fi
**Pekka Koskela**- Affiliation: Department of Mathematics, University of Jyväskylä, P.O. Box 35, FIN-40351 Jyväskylä, Finland
- MR Author ID: 289254
- Email: pkoskela@math.jyu.fi
- 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
- © Copyright 2001 American Mathematical Society
- 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
- MathSciNet review: 1845022