In this talk I will report some recent joint work with Shiguang Ma on Huber's type theorem in general dimensions. Our approach relies on our earlier work on the extension of Arsove-Huber in general dimensions. We also extend the injectivity theorem of Schoen-Yau for manifolds that admit conformal immersions into the round sphere and satisfy integral bounds on curvature.

Bio: Jie Qing received his PhD from University of California, Los Angeles in 1993 and is currently Professor at University of California, Santa Cruz. He was a Ritt Assistant Professor at Columbia University and a visiting member at the Institute for Advanced Study. Jie Qing was awarded Sloan Research Fellowships in 1999. He was Chair of Department of Mathematics at University of California, Santa Cruz in 2014-2017. He works in nonlinear analysis, harmonic analysis, and partial differential equations (systems) with applications to differential geometry, complex geometry and mathematical physics.