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

TL;DR

This paper introduces a new family of minimal surfaces in the 3-sphere with low genus, constructed via an equivariant min-max method, and analyzes their symmetry, stability, and uniqueness properties.

Contribution

It presents a novel family of minimal surfaces in the 3-sphere, constructed through a new sweepout combining the equatorial sphere and Clifford torus, with detailed symmetry and stability analysis.

Findings

New minimal surfaces with low genus discovered

Full symmetry groups determined

Lower bounds on Morse indices established

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.