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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Existence of harmonic $L^1$ functions in complete Riemannian manifolds
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by L. O. Chung PDF
Proc. Amer. Math. Soc. 88 (1983), 531-532 Request permission

Abstract:

We construct a complete Riemannian manifold which carries a nonconstant harmonic $L^1$ function.
References
  • 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, DOI 10.1007/BFb0064417
  • 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 417452, DOI 10.1512/iumj.1976.25.25051
    • 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
  • © Copyright 1983 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 88 (1983), 531-532
  • MSC: Primary 31C12; Secondary 30F20, 53C20
  • DOI: https://doi.org/10.1090/S0002-9939-1983-0699427-2
  • MathSciNet review: 699427