题目：Surface diffusion flow of axially symmetric hypersurfaces with generalised Neumann boundary conditions

报告人：Prof. James McCoy（Royal Melbourne Institute of Technology University, Australia）

时间：2026年10月14日（星期三）下午4：00-5：00

地点：双清综合楼304

摘要：We consider evolving smooth, embedded, axially symmetric hypersurfaces whose boundaries intersect two parallel hyperplanes perpendicularly.  We assume the initial hypersurface is sufficiently far from the axis and has axial curvature sufficiently small in $L^2$.  We prove that the solution to the surface diffusion flow with generalised Neumann boundary conditions beginning from this initial data exists for all time, remains axially symmetric and at a distance away from the axis, with the smallness condition preserved.  Moreover, the evolving hypersurface converges exponentially in the $C^\infty$-topology to a cylinder with the same axis and enclosing the same volume as the initial hypersurface.

报告人简介：James McCoy received his PhD in 2002 advised by Prof Klaus Ecker.  The title of his thesis was “The surface area preserving mean curvature flow”.  After post-doctoral positions with Ben Andrews and Neil Trudinger at ANU, James spent 12 years at the University of Wollongong and eight years at University of Newcastle, most recently as Deputy Head of School (Research and Research Training).  In January this year, James moved to RMIT University in Melbourne as Head of Department and Associate Dean for Mathematical and Geospatial Sciences.