An enumerative min-max theorem for minimal surfaces
Differential Geometry
2026-01-06 v1 Analysis of PDEs
Algebraic Topology
Geometric Topology
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 , 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.
Cite
@article{arxiv.2601.01736,
title = {An enumerative min-max theorem for minimal surfaces},
author = {Adrian Chun-Pong Chu and Yangyang Li and Zhihan Wang},
journal= {arXiv preprint arXiv:2601.01736},
year = {2026}
}
Comments
This paper supersedes the portion of arXiv:2507.23239v1 concerning the existence of genus 2 minimal surfaces