My research interest is about Geometric analysis, Differential geometry and PDEs.
My main research topic is Harmonic maps and related geometric flow, for example, Conformal heat flow for harmonic maps and its bubbling phenomenon.
I am currently working on various topics including harmonic map flows coupled with metric evolution, Eigenvalue estimate of Laplacian, and anayltic approaches about topology, like Rational homotopy groups.
Long Time Existence of A Flow of Elliptic Systems, joint with Lei Zhang, submitted, arXiv:2508.00551
Regularized n-Conformal heat flow and global smoothness, submitted, arXiv:2502.10679
Obstacles for Sobolev-homeomorphisms with low rank -- pointwise a.e. vs distributional Jacobians, joint with Armin Schikorra, C. R. Math. Acad. Sci. Paris 363 (2025).
Smoothness of conformal heat flow of harmonic maps, submitted, arXiv:2304.03444
Conformal heat flow of maps under Yamabe flow of metrics, joint with Hyo Seok Jang and Ki-Ahm Lee, accepted for publication in Comm. Anal. Geom.
Quantitative estimates for fractional Sobolev mappings in rational homotopy groups, joint with Armin Schikorra, Nonlinear Analysis 235 (2023): 113349.
A new conformal heat flow of harmonic maps, J. Geom. Anal. 33, 376 (2023).
Compactness of harmonic maps of surfaces with regular nodes, Ann. Glob. Anal. Geom. 64, 20 (2023).
Old papers:
A matrix sequence $\{\Gamma(A^m)\}_{m=1}^\infty$ might converge even if the matrix $A$ is not primitive, joint with Suh-Ryung Kim and Boram Park, Linear Algebra Appl., 438 (2013), 2306-2319
On the Pythagorean triple, joint with Hye Sook Park, J.Korea Soc. Math. Educ. Ser.A, 41 (2002), no.2, 227-231