报告题目：The Isometric Immersion of Surfaces with Finite Total Curvature

报告时间：2024-03-28   16:30-17:30

报  告 人 ： 韩青     教授    美国圣母大学

腾讯会议：128-437-234（同步直播）

报告地点：武大理学院东北楼四楼报告厅

Abstract：In this talk, we discuss the smooth isometric immersion of a complete simply connected surface with a negative Gauss curvature in the three-dimensional Euclidean space. For a surface with a finite total Gauss curvature and appropriate oscillations of the Gauss curvature, we prove the global existence of a smooth solution to the Gauss-Codazzi system and thus establish a global smooth isometric immersion of the surface into the three-dimensional Euclidean space. Based on a crucial observation that some linear combinations of the Riemann invariants decay faster than others, we reformulate the Gauss-Codazzi system as a symmetric hyperbolic system with a partial damping. Such a damping effect and an energy approach permit us to derive global decay estimates and meanwhile control the non-integrable coefficients of nonlinear terms.