activity
20242026
collaborators

6 papers

math.AP2026

Global existence and convergence of a density heat flow for strictly subcritical Liouville systems

Zetao Cheng, Haoyu Li, Woongbae Park +1

We study a density heat flow associated with normalized Liouville systems on a closed connected Riemannian surface, and we show that this flow leads to the existence of solutions f…

math.AP2026

Synchronized Solutions for Liouville Systems with Sign-Changing Coefficients

Woongbae Park, Lei Zhang

We consider singular Liouville systems on closed Riemann surfaces with a common sign-changing coefficient. Direct continuation from a positive coefficient is obstructed by the unav…

math.DG2026

Extrinsic bi-Conformal Heat Flow and its smoothness

Woongbae Park

In this paper we introduce conformal heat flow of (extrinsic) biharmonic maps on -manifold, simply called bi-conformal heat flow (bi-CHF), and study its properties. Similar to o…

math.AP2025

Long Time Existence of A Flow of Elliptic Systems

Woongbae Park, Lei Zhang

For elliptic systems defined on Riemann surfaces, Liouville and Toda systems represent two well-known classes exhibiting drastically different solution structures. Over the years,…

math.DG2025

Regularized -Conformal heat flow and global smoothness

Woongbae Park

In this paper, we introduce the regularized conformal heat flow of -harmonic maps, or simply regularized -conformal heat flow from -dimensional Riemannian manifold. This i…

math.AP2024

Obstacles for Sobolev-homeomorphisms with low rank -- pointwise a.e. vs distributional Jacobians

Woongbae Park, Armin Schikorra

We show that for any and there exist neither -Sobolev nor -Hölder homeomorphisms from the disk into …