Complete minimal surfaces and the puncture number problem
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- by Kichoon Yang PDF
- Proc. Amer. Math. Soc. 119 (1993), 261-265 Request permission
Abstract:
Given a nonnegative integer $g$, let $\mathcal {P}(g)$ denote the set of integers $N$ such that an arbitrary compact Riemann surface with genus $g$ can be completely conformally and minimally immersed in ${\mathbb {R}^3}$ (with finite total curvature) with exactly $N$ punctures. We prove that the infimum of $\mathcal {P}(g)$ is at most $4g$ and that the set $\mathcal {P}(g)$ may not miss any $3g$ consecutive integers larger than the infimum of $\mathcal {P}(g)$.References
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Additional Information
- © Copyright 1993 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 119 (1993), 261-265
- MSC: Primary 53A10; Secondary 30F10, 53A30
- DOI: https://doi.org/10.1090/S0002-9939-1993-1181179-X
- MathSciNet review: 1181179