Research
My research has been primarily focusing on geometric analysis and partial differential equations. I am particularly interested in the PDE theory on non-compact manifolds, especially those with singularities. Currently, my main topics are geometric flows on singular manifolds (including the Yamabe flow and the surface diffusion flow), degenerate/singular differential equations and their applications to applied mathematics (especially, image processing). Other topics I have worked on include regularity of elliptic and parabolic equations, free boundary problems (the Stefan probem), harmonic heat flow and nematic liquid crystal.
To find more details of my research, click here for my research statement.
You can find a complete list of my publications and preprints here.