Harmonic nonholomorphic maps from a surface to a sphere
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- by Luc Lemaire PDF
- Proc. Amer. Math. Soc. 71 (1978), 299-304 Request permission
Abstract:
For every p and $\mathcal {D}$ such that $|\mathcal {D}| \leqslant p - 1$, there exist a Riemann surface of genus p and a harmonic nonholomorphic map of degree $\mathcal {D}$ from that surface to the sphere. For some of the degrees, a holomorphic map exists for the same Riemann surface.References
- James Eells Jr. and J. H. Sampson, Harmonic mappings of Riemannian manifolds, Amer. J. Math. 86 (1964), 109–160. MR 164306, DOI 10.2307/2373037
- J. Eells and J. C. Wood, Restrictions on harmonic maps of surfaces, Topology 15 (1976), no. 3, 263–266. MR 420708, DOI 10.1016/0040-9383(76)90042-2
- R. C. Gunning, Lectures on Riemann surfaces, Princeton Mathematical Notes, Princeton University Press, Princeton, N.J., 1966. MR 0207977
- Luc Lemaire, Applications harmoniques de surfaces, C. R. Acad. Sci. Paris Sér. A-B 280 (1975), no. 13, Aiii, A897–A899 (French, with English summary). MR 372919
- Luc Lemaire, Applications harmoniques de surfaces riemanniennes, J. Differential Geometry 13 (1978), no. 1, 51–78 (French). MR 520601
- R. T. Smith, Harmonic mappings of spheres, Bull. Amer. Math. Soc. 78 (1972), 593–596. MR 298590, DOI 10.1090/S0002-9904-1972-13018-0
- R. T. Smith, The second variation formula for harmonic mappings, Proc. Amer. Math. Soc. 47 (1975), 229–236. MR 375386, DOI 10.1090/S0002-9939-1975-0375386-2 J. C. Wood, Harmonic mappings between surfaces, Ph. D. thesis, Univ. of Warwick, England, 1974.
Additional Information
- © Copyright 1978 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 71 (1978), 299-304
- MSC: Primary 58E99; Secondary 31C05, 53C20
- DOI: https://doi.org/10.1090/S0002-9939-1978-0501102-X
- MathSciNet review: 0501102