Motivated by the recent progress of the concentration-compactness approach in solving the energy-critical and mass-critical dispersive equations such as nonlinear Schr\”odinger equations and the nonlinear wave equations, we investigated the extremizer problem for the Tomas-Stein inequality for the two dimensional sphere. We prove that extremizers exist and they are also smooth. We also prove that constant functions are local extremizers. The method is the concentration-compactness facilitated by a refined Bourgain-type Tomas-Stein inequality. This is a joint work with Michael Christ.

报告人简介：邵双林，堪萨斯大学数学系副教授（2011--现在）。本硕（1997--2004）毕业于北京师范大学，2008获得加州大学洛杉矶分校博士学位（2004-2008）。博士后就职于普林斯顿数学高等研究所（2008-2009）和美国国家数学及其应用研究所（2009--2011）。研究方向为调和分析与偏微分方程，在国际主流数学期刊Analysis and PDE, DCDS-A, Dynamics PDEs, Indiana Univ. Math.J, JDE，EJDE, JFA，Proceedings of AMS, Advances in Mathematics, Bulletin of London Mathematical Society, Rev. Mat. Iberoamericana等发表论文19篇.