Genus two embedded minimal surfaces in S³ with dihedral symmetry · arXivDesk
2511.16295Nov 20, 202587 pages, 18 figures. This version replaces the previous paper "Genus two embedded minimal surfaces in $\mathbb{S}^3$ with bidihedral symmetry (arXiv:2511.16295v2). The hypotheses in the main theorem have been weakened from the previous paper by assuming half of the symmetries, with the same conclusion
Genus two embedded minimal surfaces in S3 with dihedral symmetry
We prove that the Lawson surface ξ2,1 is the unique closed embedded minimal surface of genus 2 in S3 whose isometry group contains the dihedral group D4
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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.