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arXiv · 2605.28504

Minimal surfaces with rapid area growth

Tobias Holck Colding·Francisco Martín·William P. Minicozzi II
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Abstract

We give examples of proper minimal immersions in Euclidean space with very rapid area growth. The first is a proper embedding into $\bf{R}^4$ that yields a stable minimal surface, while the second is a proper immersion into $\bf{R}^3$. These results are motivated by [CM1] that shows that proper minimal submanifolds confined in space satisfy strong structural constraints.

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Tobias Holck Colding, Francisco Martín, William P. Minicozzi II. 2026-05-27. Minimal surfaces with rapid area growth. https://arxiv.org/abs/2605.28504

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