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Adrian Chun-Pong Chu

Publications and source records attributed to Adrian Chun-Pong Chu.

8 recordsLinked to original sources
arXiv2026

Min-max theory and minimal surfaces with prescribed genus

We establish a general min-max type theorem that produces minimal surfaces with prescribed genus in 3-manifolds with positive Ricci curvature. An important intermediate step is to show that, in a generic metric with positive Ricci curvature, any family of surfaces with possibly finitely many singularities can be deformed into a certain topologically optimal family. Results in this paper will be crucial to our program on the construction of multiple minimal surfaces with prescribed genus in 3-spheres via topological methods.

math.DG↗
arXiv2026

An enumerative min-max theorem for minimal surfaces

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.

math.DG↗
arXiv2025

Minimal surface doublings and electrostatics for Schrödinger operators

Twenty years ago, N. Kapouleas introduced a singular perturbation construction known as "doubling", which produces sequences of high-genus minimal surfaces converging to a given minimal surface with multiplicity two. Doubling constructions have since been implemented successfully in several settings, with deep work of Kapouleas-McGrath reducing their existence theory to the problem of finding suitable families of ansatz data on the initial minimal surface. In this paper, we introduce a variational approach to the existence of minimal doublings, relating the Kapouleas-McGrath construction to the study of nondegenerate critical points for a Coulomb-type interaction energy. By analyzing the minimizers of this energy, we prove that, in a generic closed 3-manifold, every two-sided, embedded minimal surface of index one admits a sequence of minimal doublings. As a corollary, we find that a generic 3-manifold contains an infinite sequence of embedded minimal surfaces with bounded area and arbitrarily large genus, whose geometry can be described with some precision.

math.DG↗
arXiv2025

Minimal surfaces with arbitrary genus in 3-spheres of positive Ricci curvature

We describe some topological structure in the set of all surfaces with finitely many singularities in the 3-sphere. As an application, we prove that every Riemannian 3-sphere of positive Ricci curvature contains, for every g, a genus g embedded minimal surface with area at most twice the first Simon-Smith width of the ambient 3-sphere.

math.DG↗
arXiv2025

Existence of 5 minimal tori in 3-spheres of positive Ricci curvature

In 1989, B. White conjectured that every Riemannian 3-sphere has at least 5 embedded minimal tori. We confirm this conjecture for 3-spheres of positive Ricci curvature. While our proof uses min-max theory, the underlying heuristics are largely inspired by mean curvature flow.

math.DG↗
arXiv2025

Genus one singularities in mean curvature flow

We show that for certain one-parameter families of initial conditions in $\mathbb R^3$, when we run mean curvature flow, a genus one singularity must appear in one of the flows. Moreover, such a singularity is robust under perturbation of the family of initial conditions. This contrasts sharply with the case of just a single flow. As an application, we construct an embedded, genus one self-shrinker with entropy lower than a shrinking doughnut.

math.DG↗
arXiv2023

A free boundary minimal surface via a 6-sweepout

We prove that the Almgren-Pitts 6-width of the unit 3-ball is less than $2π$. We also prove that there exists a free boundary minimal surface in the unit 3-ball that has genus at most 1, index at most 5, area less than $2π$, and is not the equatorial disk or the critical catenoid.

math.DG↗