Lifespan theorem for constrained surface diffusion flows

Authors

James McCoy, University of WollongongFollow
Glen Wheeler, University of WollongongFollow
Graham Williams, University of WollongongFollow

RIS ID

57434

Publication Details

McCoy, J., Wheeler, G. & Williams, G. (2011). Lifespan theorem for constrained surface diffusion flows. Mathematische Zeitschrift, 269 (1-2), 147-178.

Abstract

We consider closed immersed hypersurfaces in R^3 and R^4 evolving by a class of constrained surface diffusion flows. Our result, similar to earlier results for the Willmore flow, gives both a positive lower bound on the time for which a smooth solution exists and a small upper bound on a power of the total curvature during this time. By phrasing the theorem in terms of concentration of curvature in the initial surface, our result holds for very general initial data and has applications to further development in asymptotic analysis for these flows.