Tongji University & ShanghaiTech University
October 28-29, 2020
2020 Tongji-ShanghaiTech joint geometry workshop
会议地点2：S408, IMS@ShanghaiTech University
组织人：Chengjian Yao, Kai Zheng
Title: Gravitating vortices and cosmic strings with singularities
Abstract: We introduce the notion of twisted gravitating vortices on a compact Riemann surface. If the genus of the Riemann surface is greater than 1 and the twisting forms have suitable signs, we prove an existence and uniqueness result for suitable range of the coupling constant. It is proved via solving a continuity path deforming the coupling constant from 0 for which the system decouples as twisted Kahler-Einstein metric and twisted vortices. Moreover, specializing to a family of twisting forms smoothing delta distribution terms, we prove the existence of singular gravitating vortices whose Kahler metric has conical singularities and Hermitian metric has parabolic singularities. In the Bogomol'nyi phase, we establish an existence result for singular Einstein-Bogomol'nyi equations, which represents cosmic strings with singularities.
Title: Some estimates on extremal metrics
Abstract: In this talk, we will present a compactness theorem on extremal metrics.
Title: Approximation of the geodesic and the affine Mabuchi functional
Title：Interior gradient estimates for prescribed curvature equation
Abstract: In this talk, we shall talk on interior gradient estimates for admissible solutions to prescribed curvature equations.