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arXiv · 2410.13687

Complete minimal surfaces with Cantor ends in minimally convex domains

Antonio Alarcon
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Abstract

We survey the recent history of the conformal Calabi-Yau problem consisting in determining the complex structures admitted by complete bounded minimal surfaces in $\mathbb{R}^3$. Moreover, we prove that for any minimally convex domain $\Omega$ in $\mathbb{R}^3$ and any compact Riemann surface $R$ there is a Cantor set $C$ in $R$ whose complement $R\setminus C$ is the complex structure of a complete proper minimal surface in $\Omega$.

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Antonio Alarcon. 2024-10-17. Complete minimal surfaces with Cantor ends in minimally convex domains. https://arxiv.org/abs/2410.13687

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