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arXiv · 2508.06019

Minimal surfaces with arbitrary genus in 3-spheres of positive Ricci curvature

Adrian Chun-Pong Chu
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Abstract

We describe some topological structure in the set of all surfaces with finitely many singularities in the 3-sphere. As an application, we prove that every Riemannian 3-sphere of positive Ricci curvature contains, for every g, a genus g embedded minimal surface with area at most twice the first Simon-Smith width of the ambient 3-sphere.

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Adrian Chun-Pong Chu. 2025-08-08. Minimal surfaces with arbitrary genus in 3-spheres of positive Ricci curvature. https://arxiv.org/abs/2508.06019

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