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arXiv:2511.16295 (math)
This paper has been withdrawn by Joaquin Perez
[Submitted on 20 Nov 2025 (v1), last revised 20 Aug 2026 (this version, v4)]

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

Authors: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.
Comments: Withdrawn by the authors because Lemma 4.2 contains a gap: the moduli space of the relevant R_2-symmetric right-angled geodesic hexagons has an additional parameter omitted from the stated classification. This affects the reduction of the closing problem, so the main theorem is not proved by the present manuscript. A corrected version is in preparation
Subjects: Differential Geometry (math.DG)
MSC classes: Primary 53A10, Secondary 49Q05, 53C42
Cite as: arXiv:2511.16295 [math.DG]
  (or arXiv:2511.16295v4 [math.DG] for this version)
  https://doi.org/10.48550/arXiv.2511.16295

Submission history

From: Joaquin Perez [view email]
[v1] Thu, 20 Nov 2025 12:18:23 UTC (1,508 KB)
[v2] Thu, 15 Jan 2026 00:17:58 UTC (1,508 KB)
[v3] Sun, 12 Jul 2026 23:55:57 UTC (2,278 KB)
[v4] Thu, 20 Aug 2026 09:54:17 UTC (1 KB) (withdrawn)
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