Status: 
Available
Level: 
PhD Project
Level: 
Masters Project
Level: 
Honours Project
Level: 
Summer Project
Supervisor(s): 
Dr Huy The Nguyen

Surfaces are 2-dimensional objects that play a fundamental role in differential geometry and its applications. When surfaces are immersed in an ambient space they have a natural associated energy called the Willmore energy (or the elastic bending energy). The projects offered here will investigate surfaces with bounds on this critical energy. In particular, we will study optimal co-ordinate systems and their possible degeneration due to concentration phenomena. We will also study various aspects pf the variational problem associated to the elastic bending energy whose critical points are Willmore surfaces.