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arXiv · 1409.6901

Embedded minimal surfaces in $\mathbb{R}^n$

Antonio Alarcon·Franc Forstneric·Francisco J. Lopez
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Abstract

In this paper, we prove that every confomal minimal immersion of an open Riemann surface into $\mathbb{R}^n$ for $n\ge 5$ can be approximated uniformly on compacts by conformal minimal embeddings. Furthermore, we show that every open Riemann surface carries a proper conformal minimal embedding into $\mathbb{R}^5$. One of our main tools is a Mergelyan approximation theorem for conformal minimal immersions to $\mathbb{R}^n$ for any $n\ge 3$ which is also proved in the paper.

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Antonio Alarcon, Franc Forstneric, Francisco J. Lopez. 2015-12-15. Embedded minimal surfaces in $\mathbb{R}^n$. https://doi.org/10.1007/s00209-015-1586-5

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