October 9, 2025Open Access

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

Puntos clave

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.

Resumen

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.

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