|Differential Geometry Seminar, Korea Institute for Advanced Study, Dr. Hojoo Lee|
Monday, January 2, 14:10—15:00 數學系3F會議室
Title: Poisson's Equation, Inverse Mean Curvature Flow, and Infinite Bottles
Abstract: While the round spheres are exceptionally rigid among compact self-expanding solitons, even in the class of rotational hypersurfaces, there are interesting examples of complete noncompact self-expanders. Indeed, G. Huisken and T. Ilmanen constructed a complete, rotationally symmetric, self-expander with one asymptotically cylindrical end. First, we use the shooting method to construct new self-expanders, so called infinite bottles, having two cylindrical ends (joint with G. Drugan and G. Wheeler). Second, we investigate the linearized operator of the soliton equation to establish the rigidity of rotational self-expanders (joint work with G. Drugan and F. Fong).
|創校85週年暨創系60週年系列演講, 清華大學數學系 蔡東和 教授|
Thursday, January 12, 16:10—17:00 數學系3174教室
Title: On a Simple Method to Derive the Hairclip and Paperclip Solutions of the Curve Shortening Flow
Abstract: We use a simple method to derive four important explicit graphical solutions of the curve shortening flow in the plane. From this method, one can immediately see that the hairclip and the paperclip solutions both converge to the Grim Reaper solutions as time tends to infinity.