Genus two embedded minimal surfaces in $\mathbb{S}^3$ with dihedral symmetry

José M. Espinar; Joaquín Pérez

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arXiv · 2511.16295

Genus two embedded minimal surfaces in $\mathbb{S}^3$ with dihedral symmetry

José M. Espinar·Joaquín Pérez

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Abstract

We prove that the Lawson surface $\xi_{2,1}$ is the unique closed embedded minimal surface of genus $2$ in $\mathbb{S}^3$ whose isometry group contains the dihedral group $D_4$ generated by two reflections across orthogonal totally geodesic two-spheres and a half-turn about a great circle. This weakens the full-symmetry hypotheses in previous characterizations of Lawson surfaces and leads to a substantially different geometric problem.

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BibTeX RIS

José M. Espinar, Joaquín Pérez. 2025-11-20. Genus two embedded minimal surfaces in $\mathbb{S}^3$ with dihedral symmetry. https://arxiv.org/abs/2511.16295

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