Year: 2026
Type: preprint
Abstract: We prove an enumerative min-max theorem that relates the number of genus g minimal surfaces in 3-manifolds of positive Ricci curvature to topological properties of the set of embedded surfaces of genus $\leq g$, possibly with finitely many singularities. This completes a central component of our program of using topological methods to enumerating minimal surfaces with prescribed genus. As an application, we show that every 3-sphere of positive Ricci curvature contains at least 4 embedded minimal surfaces of genus 2.
Source: arXiv (Cornell University)
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W7118844369
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