Choi, Kyeongsu
Professor
Partial Differential Equations
Kyeongsu Choi works on elliptic and parabolic PDEs and Geometric analysis. His research interests include singularity analysis for geometric flows. With his collaborators, he settled the mean convex neighborhood conjecture for the mean curvature flow to show the well-posedness around stable singularities. In addition, with other collaborators, he made contribution to the generic mean curvature flow by providing a way to avoid unstable singularities. He is also interested in fully nonlinear PDEs and free boundary problems. With other collaborators, he settled the Firey's conjecture for the Gauss curvature flow in all dimensions to investigate the asymptotic behavior of closed solutions.
- B.S., Mathematics, Seoul National University, Aug. 2012
- Ph.D., Mathematics, Columbia University, May 2017
- C.L.E. Moore Instructor, M.I.T., Sep. 2017 - May 2012
- Professor, KIAS, Jun. 2020 - Present
Frontiers of Science Award, ICBS, 2023
Asian Young Scientist Fellowship, 2023
Young Scientist Award, 2022
POSCO Science Fellow, 2021
Sangsan Young Mathematician Prize, 2020
Publications at KIAS
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Curvature bound for Lp Minkowski problem
ADVANCES IN MATHEMATICS, 2024 -
Enhanced profile estimates for ovals and translators
ADVANCES IN MATHEMATICS, 2024 -
Mean curvature flow with generic initial data
INVENTIONES MATHEMATICAE, 2024 -
MEAN CURVATURE FLOW WITH GENERIC LOW-ENTROPY INITIAL DATA
DUKE MATHEMATICAL JOURNAL, 2024 -
UNIQUENESS OF ANCIENT SOLUTIONS TO GAUSS CURVATURE FLOW ASYMPTOTIC TO A CYLINDER
JOURNAL OF DIFFERENTIAL GEOMETRY, 2024 -
Classification of noncollapsed translators in R-4
CAMBRIDGE JOURNAL OF MATHEMATICS, 2023 -
Ancient low-entropy flows, mean-convex neighborhoods, and uniqueness
ACTA MATHEMATICA, 2022 -
Ancient asymptotically cylindrical flows and applications
INVENTIONES MATHEMATICAE, 2022 -
The Q(k) flow on complete non-compact graphs
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2022 -
Ancient gradient flows of elliptic functionals and Morse index
AMERICAN JOURNAL OF MATHEMATICS, 2022 -
Convergence of Gauss curvature flows to translating solitons
ADVANCES IN MATHEMATICS, 2022 -
Ancient finite entropy flows by powers of curvature in R-2
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2022 -
Uniqueness of convex ancient solutions to mean curvature flow in higher dimensions
GEOMETRY & TOPOLOGY, 2021 -
CONVERGENCE OF CURVE SHORTENING FLOW TO TRANSLATING SOLITON
AMERICAN JOURNAL OF MATHEMATICS, 2021 -
TRANSLATING SOLUTIONS TO THE GAUSS CURVATURE FLOW WITH FLAT SIDES
ANALYSIS & PDE, 2021
Selected Publications
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Asymptotic behavior of flows by powers of the Gaussian curvature
Acta Mathematica 219(1), 1-16, 2017 -
Uniqueness of convex ancient solutions to mean curvature flow in R^3
Inventiones mathematicae 217(1), 35-76, 2019 -
Translating solutions to the Gauss curvature flow with flat sides
Analysis & PDE 14(2), 595-616, 2021 -
Ancient low entropy flows, mean convex neighborhoods, and uniqueness
Acta Mathematica 228(2), 217-301, 2022 -
Ancient asymptotically cylindrical flows and applications
Inventiones mathematicae 229(1), 139–241, 2022 -
Classification of noncollapsed translators in R^4
Cambridge Journal of Mathematics 11(3), 563–698, 2023 -
Mean curvature flow with generic initial data
Inventiones mathematicae, 237, 121–220, 2024 -
Mean curvature flow with generic low-entropy initial data
Duke Mathematical Journal, 173(7), 1269-1290, 2024 -
Mean curvature flow with generic initial data II
arXiv preprint 2302.08409 -
Translating surfaces under flows by sub-affine-critical powers of Gauss curvature
arXiv preprint 2104.13186
- Office: 1228 / TEL) 82-2-958-2563 /
- School of Mathematics, Korea Institute for Advanced Study
- 85 Hoegiro Dongdaemun-gu, Seoul 02455, Republic of Korea.