Abstract
In this paper we prove that, given an open Riemann surface and an integer , the set of complete conformal minimal immersions with forms a dense subset in the space of all conformal minimal immersions endowed with the compact-open topology. Moreover, we show that every domain in contains complete minimal surfaces which are dense on it and have arbitrary orientable topology (possibly infinite); we also provide such surfaces whose complex structure is any given bordered Riemann surface.
Our method of proof can be adapted to give analogous results for nonorientable minimal surfaces in , complex curves in , holomorphic null curves in , and holomorphic Legendrian curves in .
Citation
Antonio Alarcón. Ildefonso Castro-Infantes. "Complete minimal surfaces densely lying in arbitrary domains of $\mathbb{R}^n$." Geom. Topol. 22 (1) 571 - 590, 2018. https://doi.org/10.2140/gt.2018.22.571
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