Kyeongsu Choi

activity

20162026

most citedUniqueness of convex ancient solutions to mean curvature flow in higher dimensions

68 citations · 161 across the 26 of their papers we have counts for

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28 papers · 1 filter

math.DG2026

Formation and structural stability of nondegenerate neckpinches

Kyeongsu Choi, Panagiota Daskalopoulos, Natasa Sesum

In this paper, we study the formation, precise asymptotics, and structural stability of neckpinch singularities in mean curvature flow. Motivated by the static rigidity of cylindri…

math.DG2026

Ancient cylindrical flows with fast or slow convergence

Kyeongsu Choi, Robert Haslhofer

In a recent breakthrough, Bamler-Lai proved the mean-convex neighborhood conjecture in all dimensions by showing that any nontrivial ancient asymptotically cylindrical mean curvatu…

math.DG2026

Classification of ancient finite-entropy curve shortening flows

Kyeongsu Choi, Dong-Hwi Seo, Wei-Bo Su +1

We prove that any ancient smooth embedded finite-entropy curve shortening flow is one of the following: a static line, a shrinking circle, a paper clip, a translating grim reaper,…

math.DG2025

The linearized translator equation and applications

Kyeongsu Choi, Robert Haslhofer, Or Hershkovits

In this paper, we consider the linearized translator equation $L_{ϕ} u = f$ , around entire convex translators $M = graph (ϕ) \subset R^{4}$ , i.e. in the first dimension where…

math.DG2025

Revisiting ancient noncollapsed flows in $R^{3}$

Kyeongsu Choi, Robert Haslhofer

In this short paper, we give a new proof of the classification theorem for noncompact ancient noncollapsed flows in $R^{3}$ originally due to Brendle-Choi (Inventiones 2019)…

math.DG2025

Classification of ancient noncollapsed flows in $R^{4}$

Kyeongsu Choi, Robert Haslhofer

In this paper, we classify all noncollapsed singularities of the mean curvature flow in $R^{4}$ . Specifically, we prove that any ancient noncollapsed solution either is one…

math.DG2024

Continuous family of surfaces translating by powers of Gauss curvature

Beomjun Choi, Kyeongsu Choi, Soojung Kim

This paper shows the existence of convex translating surfaces under the flow by the $α$ -th power of Gauss curvature for the sub-affine-critical regime $0 < α < 1/4$ . The key aspect…

math.DG2023★ 2 cited

Curvature bound for $L_{p}$ Minkowski problem

Kyeongsu Choi, Minhyun Kim, Taehun Lee

We establish curvature estimates for anisotropic Gauss curvature flows. By using this, we show that given a measure $μ$ with a positive smooth density $f$ , any solution to the $L_p…

math.DG2023★ 1 cited

Mean curvature flow with generic initial data II

Otis Chodosh, Kyeongsu Choi, Felix Schulze

We show that the mean curvature flow of a generic closed surface in $R^{3}$ avoids multiplicity one tangent flows that are not round spheres/cylinders. In particular, we sho…

math.DG2021

Classification of noncollapsed translators in $R^{4}$

Kyeongsu Choi, Robert Haslhofer, Or Hershkovits

In this paper, we classify all noncollapsed singularity models for the mean curvature flow of 3-dimensional hypersurfaces in $R^{4}$ or more generally in $4$ -manifolds. Spec…

math.DG2021★ 12 cited

A nonexistence result for wing-like mean curvature flows in $R^{4}$

Kyeongsu Choi, Robert Haslhofer, Or Hershkovits

Some of the most worrisome potential singularity models for the mean curvature flow of $3$ -dimensional hypersurfaces in $R^{4}$ are noncollapsed wing-like flows, i.e. noncol…

math.DG2021★ 2 cited

Translating surfaces under flows by sub-affine-critical powers of Gauss curvature

Beomjun Choi, Kyeongsu Choi, Soojung Kim

We classify the surfaces translating under the flows by sub-affine-critical powers of the Gauss curvature. This, in particular, lists all translating solitons possibly model Type I…

math.DG2021★ 1 cited

Mean curvature flow with generic low-entropy initial data

Otis Chodosh, Kyeongsu Choi, Christos Mantoulidis +1

We prove that sufficiently low-entropy closed hypersurfaces can be perturbed so that their mean curvature flow encounters only spherical and cylindrical singularities. Our theorem…

math.DG2020★ 2 cited

Ancient finite entropy flows by powers of curvature in $R^{2}$

Kyeongsu Choi, Liming Sun

We show the existence of non-homothetic ancient flows by powers of curvature embedded in $R^{2}$ whose entropy is finite. We determine the Morse indices and kernels of the l…

math.DG2020★ 1 cited

Classification of ancient flows by sub-affine-critical powers of curvature in $R^{2}$

Kyeongsu Choi, Liming Sun

We classify closed convex $α$ -curve shortening flows for sub-affine-critical powers $α \leq \frac{1}{3}$ . In addition, we show that closed convex smooth finite entropy $α$ -curve sho…

math.DG2020★ 1 cited

Uniqueness of ancient solutions to Gauss curvature flow asymptotic to a cylinder

Beomjun Choi, Kyeongsu Choi, Panagiota Daskalopoulos

We address the classification of ancient solutions to the Gauss curvature flow under the assumption that the solutions are contained in a cylinder of bounded cross section. For eac…

math.DG2020★ 7 cited

Mean curvature flow with generic initial data

Otis Chodosh, Kyeongsu Choi, Christos Mantoulidis +1

We show that the mean curvature flow of generic closed surfaces in $R^{3}$ avoids asymptotically conical and non-spherical compact singularities. We also show that the mea…

math.DG2019★ 2 cited

Ancient asymptotically cylindrical flows and applications

Kyeongsu Choi, Robert Haslhofer, Or Hershkovits +1

In this paper, we prove the mean-convex neighborhood conjecture for neck singularities of the mean curvature flow in $R^{n + 1}$ for all $n \geq 3$ : we show that if a mean cu…

math.DG2019★ 35 cited

Ancient gradient flows of elliptic functionals and Morse index

Kyeongsu Choi, Christos Mantoulidis

We study closed ancient solutions to gradient flows of elliptic functionals in Riemannian manifolds, including mean curvature flow and harmonic map heat flow. Our work has various…

math.DG2019

Convergence of Gauss curvature flows to translating solitons

Beomjun Choi, Kyeongsu Choi, Panagiota Daskalopoulos

We address the asymptotic behavior of the $α$ -Gauss curvature flow, for $α > 1/2$ , with initial data a complete non-compact convex hypersurface which is contained in a cylinder of bo…

math.DG2018★ 2 cited

Ancient low entropy flows, mean convex neighborhoods, and uniqueness

Kyeongsu Choi, Robert Haslhofer, Or Hershkovits

In this article, we prove the mean convex neighborhood conjecture for the mean curvature flow of surfaces in $R^{3}$ . Namely, if the flow has a spherical or cylindrical sing…

math.DG2018

Convergence of Curve Shortening Flow to Translating Soliton

Beomjun Choi, Kyeongsu Choi, Panagiota Daskalopoulos

This paper concerns with the asymptotic behavior of complete non-compact convex curves embedded in $R^{2}$ under the $α$ -curve shortening flow for exponents $α > \frac{1}{2}$ . We…

math.DG2018★ 68 cited

Uniqueness of convex ancient solutions to mean curvature flow in higher dimensions

S. Brendle, K. Choi

In this paper, we consider noncompact ancient solutions to the mean curvature flow in $R^{n + 1}$ ( $n \geq 3$ ) which are strictly convex, uniformly two-convex, and noncollap…

math.DG2016

Asymptotic behavior of flows by powers of the Gaussian curvature

Simon Brendle, Kyeongsu Choi, Panagiota Daskalopoulos

We consider a one-parameter family of strictly convex hypersurfaces in $R^{n + 1}$ moving with speed $- K^{α} ν$ , where $ν$ denotes the outward-pointing unit normal vector and…

Formation and structural stability of nondegenerate neckpinches

Ancient cylindrical flows with fast or slow convergence

Classification of ancient finite-entropy curve shortening flows

The linearized translator equation and applications

Revisiting ancient noncollapsed flows in R3

Classification of ancient noncollapsed flows in R4

Continuous family of surfaces translating by powers of Gauss curvature

Curvature bound for Lp​ Minkowski problem

Mean curvature flow with generic initial data II

Classification of noncollapsed translators in R4

A nonexistence result for wing-like mean curvature flows in R4

Translating surfaces under flows by sub-affine-critical powers of Gauss curvature

Mean curvature flow with generic low-entropy initial data

Ancient finite entropy flows by powers of curvature in R2

Classification of ancient flows by sub-affine-critical powers of curvature in R2

Uniqueness of ancient solutions to Gauss curvature flow asymptotic to a cylinder

Mean curvature flow with generic initial data

Ancient asymptotically cylindrical flows and applications

Ancient gradient flows of elliptic functionals and Morse index

Convergence of Gauss curvature flows to translating solitons

Ancient low entropy flows, mean convex neighborhoods, and uniqueness

Convergence of Curve Shortening Flow to Translating Soliton

Uniqueness of convex ancient solutions to mean curvature flow in higher dimensions

Asymptotic behavior of flows by powers of the Gaussian curvature

Revisiting ancient noncollapsed flows in $R^{3}$

Classification of ancient noncollapsed flows in $R^{4}$

Curvature bound for $L_{p}$ Minkowski problem

Classification of noncollapsed translators in $R^{4}$

A nonexistence result for wing-like mean curvature flows in $R^{4}$

Ancient finite entropy flows by powers of curvature in $R^{2}$

Classification of ancient flows by sub-affine-critical powers of curvature in $R^{2}$