Embedded minimal surfaces of finite topology. (English) Zbl 1420.53015
Summary: In this paper we prove that a complete, embedded minimal surface \(M\) in \(\mathbb{R}^{3}\) with finite topology and compact boundary (possibly empty) is conformally a compact Riemann surface \(\overline{M}\) with boundary punctured in a finite number of interior points and that \(M\) can be represented in terms of meromorphic data on its conformal completion \(\overline{M}\). In particular, we demonstrate that \(M\) is a minimal surface of finite type and describe how this property permits a classification of the asymptotic behavior of \(M\).
MSC:
| 53A10 | Minimal surfaces in differential geometry, surfaces with prescribed mean curvature |
| 30F99 | Riemann surfaces |
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