An introduction to the curvature equation in a compact Riemann surface
In this talk, I will briefly introduce the singular Liouville equation which originates from the conformal geometry. When the parameter is critical, it has a deep interaction with integrable
Lame equation. In such a case, the issue arised from PDE can be translated to study the monodromy representation of the relevant Lame equation. From here, the aspect of integrable system comes in, which riches this PDE as well as the geometric problem with Painleve equation.
Chang, Shu-Cheng (NTU)
Kuo, Ting-Jung (NTNU)
Lin, Chun-Chi (NTNU)