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Harmonic functions on a Riemannian ball

Published online by Cambridge University Press:  24 October 2008

Mitsuru Nakai  and
Leo Sario
Mitsuru Nakai
Affiliation:
Nagoya Institute of Technology and University of California, Los Angeles
Leo Sario
Affiliation:
Nagoya Institute of Technology and University of California, Los Angeles
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Extract

Consider the classes OHX of noncompact Riemannian manifolds M of dimension N ≥ 2 carrying no non-constant harmonic functions with properties X = P (positive), B (bounded), D (Dirichlet finite), or BD (B and D). Denote by OG the class of parabolic manifolds of dimension N ≥ 2. The following complete string of strict inclusion relations is known:

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 80 , Issue 2 , September 1976 , pp. 277 - 282
Copyright
Copyright © Cambridge Philosophical Society 1976

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References

REFERENCES

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