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Complete minimal surfaces and the puncture number problem


Author: Kichoon Yang
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
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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)$.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1993-1181179-X
Article copyright: © Copyright 1993 American Mathematical Society

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