Research Interests

I am a mathematician, my research interests has evolved over the years--in the early stage of my career, I am interested in problems in classical harmonic analysis studying local and boundary behavior of functions under global constraints. Gradually my interest shifts to problems in geometric analysis--using methods in analysis in particular the tool of partial differential equations to study problems in differential geometry. In recent year, the main focus of my research interest is in "conformal geometry", a recent project is to generalize the classical uniformization theorem from compact surfaces to a class of four dimensional spaces according to the sign of some conformally invariant geometric quantities, in particular to recognize the four dimensional sphere. The problem is ultimately related to the problems in conformal field theory in mathematical physics.

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Section 11: Mathematics