On the Flow of Non-Axisymmetric Perturbations of Cylinders via Surface Diffusion

We study the surface diffusion flow acting on a class of general (non–axisymmetric) perturbations of cylinders Cr in IR3. Using tools from parabolic theory on uniformly regular manifolds, and maximal regularity, we establish existence and uniqueness of solutions to surface diffusion flow starting from (spatially–unbounded) surfaces defined over Cr via scalar height functions which are uniformly bounded away from the central cylindrical axis. Additionally, we show that Cr is normally stable with respect to 2π–axially–periodic perturbations if the radius r > 1,and unstable if 0 < r < 1. Stability is also shown to hold in settings with axial Neumann boundary conditions.