Minimal immersions of punctured compact Riemann surfaces in $\textbf {R}^ 3$
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- by Kichoon Yang PDF
- Proc. Amer. Math. Soc. 113 (1991), 809-816 Request permission
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.References
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Additional Information
- © Copyright 1991 American Mathematical Society
- 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