Topic: The Isometric Immersion of Surfaces with Finite Total Curvature

Lecturer: Professor Han Qing (University of Notre Dame, USA)

Time: 9:00-12:00am, Thursday, March 28, 2024, UTC+8

Venue: Room 213 of the Mathematics and Statistics Building, School of Science, the South Lake Campus

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.

Biography: Qing Han is a tenured professor in the Department of Mathematics at the University of Notre Dame (USA). Dr. Han received his Ph.D. from the Courant Institute of Mathematics, New York University, and a postdoctoral fellowship from the University of Chicago. He is a Sloan Research Fellow, and has been working on nonlinear partial differential equations and geometric analysis for a long time, and has made a series of original and important research results in equidistant embedding, Monge-Ampere equations, zerosets and singular sets of harmonic functions, degenerate equations, etc.

Edited by: Li Tiantian

Source: School of Science