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Minimal immersions of punctured compact Riemann surfaces in $ {\bf R}\sp 3$


Author: Kichoon Yang
Journal: Proc. Amer. Math. Soc. 113 (1991), 809-816
MSC: Primary 53A10; Secondary 30F10, 49Q10, 53C42
DOI: https://doi.org/10.1090/S0002-9939-1991-1069297-6
MathSciNet review: 1069297
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Abstract: We prove that a hyperelliptic Riemann surface of genus $ g$ can be completely conformally and minimally immersed in $ {R^3}$ with finite total curvature with at most $ 3g + 2$ punctures; an arbitrary compact Riemann surface of genus $ g$ can be so immersed with at most $ 4g$ punctures. Moreover, we show that there is at least a one-parameter family of nonisometric such immersions for a given punctured compact Riemann surface. Our results improve earlier results of Gackstatter-Kunert and the author.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1991-1069297-6
Article copyright: © Copyright 1991 American Mathematical Society

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