4 papers
Lipschitz regularity of harmonic map heat flows from spaces into spaces
Bang-Xian Han, Hui-Chun Zhang, Xi-Ping Zhu
We prove positive-time regularity for harmonic map heat flows from finite-dimensional spaces into complete spaces, without assuming that eithe…
One-phase Free Boundary Problems on RCD Metric Measure Spaces
Chung-Kwong Chan, Hui-Chun Zhang, Xi-Ping Zhu
In this paper, we consider a vector-valued one-phase Bernoulli-type free boundary problem on a metric measure space with Riemannian curvature-dimension condition $RCD(K,…
Lipschitz regularity of harmonic map heat flows into spaces
Hui-Chun Zhang, Xi-Ping Zhu
In 1964, Eells and Sampson proved the celebrated long-time existence and convergence for the harmonic map heat flow into non-positively curved Riemannian manifolds. In 1992, Gromov…
Optimal boundary regularity of harmonic maps from -spaces to -spaces
Hui-Chun Zhang, Xi-Ping Zhu
In 1983, Schoen-Uhlenbeck \cite{SU83} established boundary regularity for energy-minimizing maps between smooth manifolds with the Dirichlet boundary condition under the assumption…