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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
DOI: https://doi.org/10.1090/S0002-9939-1978-0501102-X
MathSciNet review: 0501102
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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.


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Keywords: Harmonic maps, holomorphic map
Article copyright: © Copyright 1978 American Mathematical Society