题目：The Isometric Immersion of Surfaces with Finite Total Curvature

报告人：韩青 教授（美国诺特丹大学👩🏽‍🔬👩🏽‍🎓、北京大学）

时间：2024年4月2日15😬：30-16:30

地点：致远楼101室

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 oscilla- tions 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.

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