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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Existence of harmonic $ L^1$ functions in complete Riemannian manifolds


Author: L. O. Chung
Journal: Proc. Amer. Math. Soc. 88 (1983), 531-532
MSC: Primary 31C12; Secondary 30F20, 53C20
MathSciNet review: 699427
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Abstract: We construct a complete Riemannian manifold which carries a nonconstant harmonic $ L^1$ function.


References [Enhancements On Off] (What's this?)

  • [1] Leo Sario, Mitsuru Nakai, Cecilia Wang, and Lung Ock Chung, Classification theory of Riemannian manifolds, Lecture Notes in Mathematics, Vol. 605, Springer-Verlag, Berlin-New York, 1977. Harmonic, quasiharmonic and biharmonic functions. MR 0508005 (58 #22612)
  • [2] Shing Tung Yau, Some function-theoretic properties of complete Riemannian manifold and their applications to geometry, Indiana Univ. Math. J. 25 (1976), no. 7, 659–670. MR 0417452 (54 #5502)
  • [3] L. Karp, Subharmonic functions, harmonic mappings and isometric immersions, Seminar of Differential Geometry (S. T. Yau, editor), Princeton Univ. Press, Princeton, N. J., 1982.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1983-0699427-2
PII: S 0002-9939(1983)0699427-2
Article copyright: © Copyright 1983 American Mathematical Society