Minimal surfaces with rapid area growth
Differential Geometry
2026-05-28 v1 Analysis of PDEs
Abstract
We give examples of proper minimal immersions in Euclidean space with very rapid area growth. The first is a proper embedding into that yields a stable minimal surface, while the second is a proper immersion into . These results are motivated by [CM1] that shows that proper minimal submanifolds confined in space satisfy strong structural constraints.
Cite
@article{arxiv.2605.28504,
title = {Minimal surfaces with rapid area growth},
author = {Tobias Holck Colding and Francisco Martín and William P. Minicozzi},
journal= {arXiv preprint arXiv:2605.28504},
year = {2026}
}