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.
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