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This is a Quantitative Study study.

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October 16, 2025Open Access

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

Key Points

Every Riemannian 3-sphere with positive Ricci curvature contains minimal surfaces of any genus.
The area of these minimal surfaces is at most twice the first Simon-Smith width of the ambient space.
Surfaces studied possess finitely many singularities, demonstrating specific topological structure.
This research enriches understanding of minimal surfaces within the context of Riemannian geometry.

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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Cite This Study

Adrian Chun-Pong Chu (Fri,) studied this question.

synapsesocial.com/papers/68f10ecee6a12fd042899a2b https://doi.org/https://doi.org/10.48550/arxiv.2508.06019

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