The Isometric Immersion of Surfaces with Finite Total Curvature

主講人：韓青 美國圣母大學數(shù)學系終身教授

時間：2024年4月11日16：00

地點：三號樓332室

舉辦單位：數(shù)理學院

主講人介紹：韓青，美國圣母大學數(shù)學系終身教授。美國紐約大學庫朗數(shù)學研究所博士，美國芝加哥大學博士后。獲美國Sloan Research Fellowship. 韓青教授長期致力于非線性偏微分方程和幾何分析的研究，在等距嵌入、Monge-Ampere方程、調(diào)和函數(shù)的零點集和奇異集、退化方程等方面做出了一系列原創(chuàng)性的重要研究成果。

內(nèi)容介紹：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.