國立清華大學 數學系

Abstract: A curvature equation so called the mean field equation is a classical topic in conformal geometry and elliptic PDEs, while Painleve VI equation is a classical topic in Integrable system and complex ODEs. It is the first time that we develop a theory to connect these two areas. In this talk, I will first concern the mean field equation with large parameter and give a positive result about the existence and then go to small parameter case. Surprisingly, it would relate bubbling solutions of the mean field equation with Painleve VI equation via isomonodromic deformation of Lame equation. We succeed to give a criterion of the existence of solutions to the small parameter case. Tea Time: 3:30PM, R707