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arXiv · 2610.32111

Minimal Surfaces in $\mathbb{R}^4$ with Three Planar Ends II: Symmetry and Nonexistence

Jaehoon Lee·Eungbeom Yeon
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Abstract

In this paper, we study complete minimal surfaces in $\mathbb{R}^4$ with three embedded planar ends parallel to those of the union of the Lagrangian catenoid and the plane containing its waist circle. We prove that no such complete embedded minimal surface of genus $g\geq 2$ with finite total curvature admits at least $4(g+1)$ symmetries. This contrasts sharply with the genus-one case, where highly symmetric examples do exist and are uniquely determined up to scaling and rigid motion.

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Jaehoon Lee, Eungbeom Yeon. 2026-10-23. Minimal Surfaces in $\mathbb{R}^4$ with Three Planar Ends II: Symmetry and Nonexistence. https://arxiv.org/abs/2610.32111

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