韩  青  教授学术报告

Title: The Isometric Immersion of Surfaces with Finite Total Curvature

Speaker: Qing Han (韩青)

Affiliation: University of Notre Dame, USA (美国圣母大学）

Time: 15:30-16:30, Thursday, 21st May, 2024 (UTC+8, Beijing Time)

Venue: Room 1502, Yifu Architecture Building, Sipailou Campus of Southeast University, Nanjing

           （东南大学四牌楼校区逸夫建筑馆丘成桐中心1502室）

Inviter: Feida Jiang（蒋飞达）

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.

Speaker

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。