Research Interests
My research is in geometric analysis, with an emphasis on rigidity and convergence. I study Riemannian manifolds with curvature bounds, particularly the geometric information carried by Green functions and the asymptotic structure of Einstein manifolds and manifolds with curvature lower bounds. I also work on quantitative isoperimetric inequalities and the convergence of geometric gradient flows, with an interest on their applications. My current interests include mean curvature flow with free boundary and the degeneration of Einstein manifolds. A recurring theme across topics is the study of uniqueness of limits and quantitative estimates for convergence, both for geometric flows and for manifolds approaching singular spaces.
Publications & Preprints
Weighted volume monotonicity and isoperimetric comparison under a lower Ricci curvature bound, with Keomkyo Seo, preprint. (ArXiv link)
Rigidity and volume pinching for the sharp gradient estimate in positive Ricci curvature, with Junyoung Kim, preprint. (ArXiv link)
Rigidity of the gradient estimate for Einstein manifolds, with Sanghoon Lee, Journal of Geometric Analysis, Volume 36 (2026), Article 316. (ArXiv link)(journal link)
Quantitative estimates for the relative isoperimetric problem and its gradient flow outside convex bodies in the plane, with Elena Mäder-Baumdicker, Robin Neumayer, and Melanie Rupflin, preprint. (ArXiv link)
Geometric medians on product manifolds, with Kisung You, Journal of Multivariate Analysis, Volume 215 (2026), Article 105653. (ArXiv link)(journal link)
Quantitative rigidity using Colding's monotonicity formulas for Ricci curvature, with Christine Breiner, Journal of Functional Analysis, Volume 291 (2026), Issue 5, Article 111537. (ArXiv link)(journal link)
Monotonicity formulas and Hessian of the Green function, Communications in Analysis and Geometry, Volume 33 (2025), Number 10, 2445--2459. (ArXiv link)(journal link)
A Matrix Li-Yau-Hamilton estimate for the Green function on Kähler manifolds, International Mathematics Research Notices, Volume 2024 (2024), Issue 10, 8230--3239. (ArXiv link) (journal link)
Canonical Identification at Infinity for Ricci-flat Manifolds, Journal of Geometric Analysis, Volume 32 (2022), Article 8. (ArXiv link)(journal link)
A Compactness Theorem for Rotationally Symmetric Riemannian Manifolds with Positive Scalar Curvature, with Wenchuan Tian and Changliang Wang, Pure and Applied Mathematics Quarterly, Volume 14 (2019), Number 3--4, 529--561. (ArXiv link)(journal link)
Matrix Inequality for the Laplace Equation, International Mathematics Research Notices, Volume 2019 (2019), Issue 11, 3485--3497. (ArXiv link)(journal link)
Awards and Grants
18th POSCO Science Fellow, 2027-2028
KAIST College of Natural Sciences Excellence in Teaching Award, 2025
Korea Women in Mathematical Sciences Outstanding Young Woman in Mathematics Award (젊은여성수학자상), 2024
NRF Grant (Outstanding Early-Career Program: 우수신진연구), 2024-2027
KAIST Startup Grant, 2023-