About: I am a H. C. Wang assistant professor (postdoc) at Cornell University. Previously I was a Gamelin Postdoctoral Fellow at SLMath (MSRI) in Fall 2024. I obtained my PhD in mathematics at the University of Chicago, supervised by André Neves.
E-mail: cc2938@cornell.edu
Research interests: minimal surface, min-max theory, geometric flow
In Fall 2026, I will be on the tenure track job market.
Research summary
Enumerative problems for minimal surfaces of prescribed genus. It was conjectured by B. White (1989) that every Riemannian 3-sphere contains at least 5 minimal tori. Joint with Y. Li, we confirmed this for metrics of positive Ricci curvature using min-max theory [link]. Recently, I also showed that every Ricci-positive 3-sphere contains a genus g minimal surface for every g [link]. See this page for an introduction.
Gluing construction for minimal surfaces. Joint with D. Stern, we proved that every Riemannian 3-manifold with generic metric contains infinitely minimal surfaces with bounded area [link]. Our proof uses the doubling construction developed by Kapouleas-McGarth. In particular, this gives a new solution to Yau's conjecture (1982) in the generic metric setting.
Singularities in geometric flow. Together with A. Sun, we found some topological criteria that ensures the appearance of some genus one singularity in mean curvature flow [link]. As an application, we constructed a genus one self-shrinker with entropy less than the shrinking doughnut.
Resources
Popular math: The romance of mathematics (Chinese)
Papers
An enumerative min-max theorem for minimal surfaces (with Yangyang Li and Zhihan Wang)
Minimal surface doublings and electrostatics of Schrödinger operators (with Daniel Stern)
Minimal surfaces with arbitrary genus in 3-spheres of positive Ricci curvature
Min-max theory and minimal surfaces with prescribed genus (with Yangyang Li and Zhihan Wang)
Existence of 5 minimal tori in 3-spheres of positive Ricci curvature (with Yangyang Li)
Strong multiplicity one theorems and homological min-max theory (with Yangyang Li)
Adv. Math. (2025)
Geom. Topol. (2025)
J. Geom. Anal. (2023)