第一场

报告题目：Curve diffusion with generalised Neumann boundary conditions inside cones

时间：2024年5月24日(周五）下午2:30-3:30      地点：理科楼A304

报告人：Professor James Mccoy ( University of Newcastle)

摘要：We study families of smooth regular planar curves satisfying the fourth order nonlinear curve diffusion flow with generalised Neumann  boundary conditions inside cones.  We show that if the initial curve has sufficiently small oscillation of curvature, then this remains so under the flow.  Such families of evolving curves either exist for a finite time, when an end of the curve has reached the tip of the cone or the curvature has become unbounded in $L^2$, or they exist for all time and converge exponentially to a circular arc that, together with the cone boundary, encloses the same area as that enclosed by the initial curve and cone boundary.  The same kind of result holds for the higher order polyharmonic curve diffusion flows with appropriate boundary conditions; in particular in the sixth order case the smallness condition on the oscillation of curvature is exactly the same as for curve diffusion.

报告人简介：James McCoy completed his PhD in mathematics in 2002 under the supervision of Klaus Ecker at Monash University.  The title of his thesis was "The surface area preserving mean curvature flow".  After completing post doctoral positions at the Australian National University with Ben Andrews and Neil Trudinger, in 2005 James moved to the University of Wollongong to become a lecturer.  In January 2018 he moved to the University of Newcastle; becoming Deputy Head of School (Research Training) in 2024.  He is also Deputy Director of the Australian Mathematical Sciences Institute and Deputy Editor of the Journal of the Australian Mathematical Society.

第二场

报告题目： A Heintze-Karcher-type inequality for capillary hypersurfaces in a hyperbolic half-space

时间：2024年5月24日(周五）下午4:00-5:00                                地点：理科楼A304

报告人：韦勇教授 （中国科学技术大学）

摘要：We establish a Heintze-Karcher-type inequality for compact embedded capillary hypersurfaces in a hyperbolic half-space. The proof uses a foliation of the enclosed domain by a family of parallel hypersurfaces with respect to a Randers type metric, which is a special Finsler metric.  As an application, we obtain an Alexandrov-type theorem for compact embedded capillary hypersurfaces of constant higher-order mean curvature in a hyperbolic half-space. This is a joint work with Yingxiang Hu, Chao Xia and Tailong Zhou.

报告人简介：韦勇，中国科学技术大学数学科学学院特任教授，博士生导师，入选国家级青年人才项目。2014年从清华大学博士毕业，博士导师是李海中教授。2014 - 2018先后在英国伦敦大学学院和澳大利亚国立大学做博士后研究。2019-2020任澳大利亚国立大学ARC研究员。2020年获国家创新人才计划青年项目回国入职中国科学技术大学。研究方向是微分几何，几何分析。研究课题包括7维流形上G2结构的几何流，超曲面上的曲率流及几何不等式。

邀请人：李海中，马辉，陈大广