Time：15:00-16:00, Wednesday, October 21 2026
Venue: E14-301
Speaker：James McCoy, The University of Newcastle
Title：Surface diffusion flow of axially symmetric hypersurfaces with generalised Neumann boundary conditions
Abstract：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.
