The Isometric Immersion of Surfaces with Finite Total Curvature
科研大讨论系列报告
报告题目(Title)：The Isometric Immersion of Surfaces with Finite Total Curvature
报告人(Speaker)：黄飞敏 研究员（中国科学院数学与系统科学研究院）
地点(Place)：后主楼1124
时间(Time)：2024年7月10日上午10:00-11:00
邀请人(Inviter)：许孝精
报告摘要
In this paper, we study 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. This is a joint work with Qing Han, Wentao Cao and Dehua Wang.
