Liouville theorems for exponentially harmonic functions on Riemannian manifolds. (English) Zbl 0771.53020
From the author’s abstract: “Suppose that \(M\) is a complete Riemannian manifold with nonnegative sectional curvature. We prove that any bounded exponentially harmonic function on \(M\) is a constant function”.
Reviewer: J.Eells (Cambridge)
Keywords:
exponentially harmonic functionReferences:
| [1] | [C] S. Y. Cheng,Liouville theorem for harmonic maps, Proc. Sympos. Pure Math.36 (1980), 147–151 · Zbl 0455.58009 |
| [2] | [Ch] H. I. Choi,On the Liouville theorem for harmonic maps, Proc. Amer. Math. Soc.85 (1982), 91–94 · Zbl 0485.53038 · doi:10.1090/S0002-9939-1982-0647905-3 |
| [3] | [DE] D. M. Duc and J. Eells,Regularity of exponentially harmonic functions, to appear in Inter. J. Math. · Zbl 0751.58007 |
| [4] | [EL] J. Eells and L. Lemaire,Another report on harmonic maps, Bull. London Math. Soc.20 (1988), 385–524 · Zbl 0669.58009 · doi:10.1112/blms/20.5.385 |
| [5] | [ES] J. Eells and J. H. Sampson,Harmonic mappings of Riemannian manifolds, Amer. J. Math.86 (1964), 109–160 · Zbl 0122.40102 · doi:10.2307/2373037 |
| [6] | [GW] R. Greene and H. Wu,Function theory of manifolds which possess a pole, Lectures notes in Math. vol. 699, Springer-Verlag, Berlin and New York, 1979 · Zbl 0414.53043 |
| [7] | [Hi] S. Hildebrandt,Liouville theorems for harmonic mappings, and an approach to Bernstein theorems, Seminar on differential geometry, ed. S. T. Yau, Princeton N.J., University Press. (1982), 107–131 · Zbl 0505.58014 |
| [8] | [Ho] M. C. Hong,On the conformal equivalence of harmonic maps and exponentially harmonic maps, To appear in Bull. London Math. Soc. (1992) |
| [9] | [Y] S. T. Yau,Harmonic functions on complete Riemannian manifolds, Comm. Pure Appl. Math.28 (1975), 201–228 · doi:10.1002/cpa.3160280203 |
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