The Isometric Immersion of Surfaces with Finite Total Curvature


主讲人:韩青 美国圣母大学数学系终身教授




主讲人介绍:韩青,美国圣母大学数学系终身教授。美国纽约大学库朗数学研究所博士,美国芝加哥大学博士后。获美国Sloan Research Fellowship. 韩青教授长期致力于非线性偏微分方程和几何分析的研究,在等距嵌入、Monge-Ampere方程、调和函数的零点集和奇异集、退化方程等方面做出了一系列原创性的重要研究成果。

内容介绍: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.