Differential Geometry Seminar
I will report on our recent research. In "Rigidity and Gap theorem for Liouville's equation", Weiming Shen and Yue Wang studied the first global term in the expansion of the solution at the boundary. In particular, they studied the global term for domains homeomorphic to the punctured disk. We found an elementary proof to their result and extended it for domains homeomorphic to annulus. I will also briefly talk about the higher dimensional case if time permits.