Chunqin Zhou

Super-Liouville Equations on Closed Riemann Surfaces

Motivated by the supersymmetric extension of Liouville theory in the recent physics literature, we couple the standard Liouville functional with a spinor field term. The resulting functional is conformally invariant. We study geometric and analytic aspects of the resulting Euler–Lagrange equations, culminating in a blow up analysis.

A local estimate for super-Liouville equations on closed Riemann surfaces

Continuing our work on the super-Liouville equations, a variational problem motivated by the supersymmetric extension of the Liouville functional in quantum field theory, we study the profile of blow-up solutions near the blow-up point and establish a local estimate for the bubbling sequences.

On stable quasi-harmonic maps and Liouville type theorems

We consider Liouville type problems of stable quasi-harmonic maps, by stable we mean that the second variation of quasi-energy functional Eq (u) is nonnegative, and we prove that the stable quasi-harmonic maps must be constant under some geometry conditions.