Research Areas
My research interests are partial differential equations and geometric analysis.
My research has been primarily focusing on geometric analysis and partial differential equations.
Currently, the main topics of my research are the study of differential operator theory on singular manifolds (especially maximal regularity theory), and geometric flows on non-compact especially singular manifolds (including the Yamabe flow, the harmonic map heat flow, the mean curvature flow, the surface diffusion flow and the Willmore flow), and nonlocal diffusions on singular manifolds (including the fractional porous medium equation and nonlocal denoising models), and free boundary problems (including the Stefan problem, two-phase Navier-Stokes equations), and relativistic viscous fluids.
