October 9, 2025Open Access

Existence of genus 2 minimal surfaces in 3-spheres. I

Key Points

Every 3-sphere with positive Ricci curvature contains at least one embedded minimal surface of genus 2.
The study establishes a connection between the existence of genus g minimal surfaces and topological properties of embedded singular surfaces.
This result extends to more general 3-manifolds, suggesting deeper links between geometry and topology.
Understanding minimal surfaces is crucial for advancements in differential geometry and topology.

Abstract

We prove that every 3-sphere of positive Ricci curvature contains some embedded minimal surface of genus 2. We also establish a theorem for more general 3-manifolds that relates the existence of genus g minimal surfaces to topological properties regarding the set of all embedded singular surfaces of genus g.

Read Full Paperexternally

Bookmark

View Full Paper

Cite This Study

Chu et al. (Thu,) studied this question.

synapsesocial.com/papers/68e70db790569dd607ee672b https://doi.org/https://doi.org/10.48550/arxiv.2507.23239

Also Consider

Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

Bookmark

View Full Paper