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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
  • [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,
  • [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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Article copyright: © Copyright 1983 American Mathematical Society

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