A new family of minimal surfaces of even genus in the three-dimensional sphere

2025/07/30 by Schulz, Mario B., Wiygul, David
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2507.22531

Abstract

We discover a family of closed, embedded minimal surfaces in the three-dimensional round sphere which includes new examples with low genus. The existence proof relies on an equivariant min-max procedure applied to a novel sweepout which is constructed by fusing the equatorial sphere with the Clifford torus. We determine the full symmetry groups of our surfaces, prove lower bounds on their Morse indices, and show that they are geometrically distinct from all previously known examples.

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Related

• Minimal surfaces in the three dimensional sphere with high symmetry
• Minimal surfaces in the three-Sphere by doubling the Clifford Torus
• Minimal surfaces in the 3-sphere by doubling the Clifford torus over\n rectangular lattices
• New minimal surface doublings of the Clifford torus and contributions to questions of Yau
• New low-genus desingularizations of three Clifford tori and related characterizations