Motion of surfaces by curvature

                                   by

              Gieri Simonett, Vanderbilt University, Nashville

                 INSCC 110, 3:30pm  Monday, June 1st, 1998


                                Abstract


I will introduce several geometric evolution laws for motion of 
surfaces driven by curvature. These will include the Mullins-Sekerka model,
the volume preserving mean curvature flow, and the surface diffusion flow.
I will present recent existence, uniqueness, and stability results. 
Numerical simulations are provided that exhibit the creation of 
singularities for curves and surfaces. Moreover, it will be shown 
that the surface diffusion flow and the volume preserving mean 
curvature flow can cause a loss of embeddedness for initially 
embedded hypersurfaces.


Requests for preprints and reprints to: simonett@math.vanderbilt.edu
This source can be found at http://www.math.utah.edu/applied-math/