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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Harmonic nonholomorphic maps from a surface to a sphere


Author: Luc Lemaire
Journal: Proc. Amer. Math. Soc. 71 (1978), 299-304
MSC: Primary 58E99; Secondary 31C05, 53C20
MathSciNet review: 0501102
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Abstract: For every p and $ \mathcal{D}$ such that $ \vert\mathcal{D}\vert \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.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1978-0501102-X
PII: S 0002-9939(1978)0501102-X
Keywords: Harmonic maps, holomorphic map
Article copyright: © Copyright 1978 American Mathematical Society