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arXiv · 2601.01736

An enumerative min-max theorem for minimal surfaces

Adrian Chun-Pong Chu·Yangyang Li·Zhihan Wang
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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.

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Adrian Chun-Pong Chu, Yangyang Li, Zhihan Wang. 2026-01-05. An enumerative min-max theorem for minimal surfaces. https://arxiv.org/abs/2601.01736

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