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发布时间:2020-08-07【告诉好友】 【关闭窗口】

  会议时间:2020/8/8 09:00-12:00

  腾讯会议ID:219 275 888

  报告人: 桂长峰 教授 (德克萨斯大学圣安东尼奥分校、中南大学)

  报告题目:New Sharp Inequalities in Analysis and Geometry

  报告摘要:The classical Moser-Trudinger inequality is a borderline case of Soblolev inequalities and has important applications in geometric analysis and PDEs. On the two dimensional sphere, Aubin in 1979 showed that the best constant in the Moser-Trudinger inequality can be reduced by half if the functions are restricted to a subset of the Sobolev space  with mass center of the functions at the origin, while Onofri in 1982 discovered an elegant optimal form of Moser-Trudinger inequality. In this talk, I will present new sharp inequalities which are variants of Aubin and Onofri inequalities on the sphere with or without constraints.

  One such inequality, for example, incorporates the mass center deviation (from the origin) into the optimal inequality of Onofri on the sphere. In another view point, this inequality also generalizes to the sphere the Lebedev-Milin inequality and the second inequality in the Szegö limit theorem on the Toeplitz determinants on the circle, which is useful in the study of isospectral compactness for metrics defined on compact surfaces, among other applications.

  The talk is based on a joint work with Amir Moradifam (University of California, Riverside) and a recent joint work with Alice Chang (Princeton).

  报告人简介:桂长峰教授1984年本科毕业北京大学,1987年得到北京大学硕士学位,1991年在美国明尼苏达大学获博士学位。曾任纽约大学库郎研究所讲师,加拿大哥伦比亚大学助教、副教授,美国康尼迪格大学副教授、教授、德克萨斯大学圣安东尼奥分校教授。他于2007年入选教育部长江学者讲座教授、2011年入选国家“千人计划”专家。他主要从事偏微分方程理论研究,特别是对Allen-Cahn方程的研究上取得了一系列在国际上有影响的工作,在国际一流数学学术期刊发表论文50余篇,其中包括 Annals of Mathematics、Inventiones Mathematicae 等顶级期刊。同时他在图像处理方面也有很好的工作, 他与合作者撰写的论文Distance Regularized Level Set Evolution and Its Application to Image Segmentation 获得了2015年IEEE SIGNAL PROCESSING SOCIETY颁发的最佳论文奖。