数学物理研讨班:The Isometric Immersion of Surfaces with Finite Total Curvature

中科院数学与系统科学研究院

数学研究所

学术报告

数学物理研讨班

报告人：韩青 教授 (University of Notre Dame )

题  目：The Isometric Immersion of Surfaces with Finite Total Curvature

时  间：2024年5月16日（星期四）10：00-11：00

地  点：数学院南楼N933

摘  要： 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.