Calculus of Variations

Much of my older work concerns geometric problems in partial differential equations and the calculus of variations. Problems of this form are often motivated from materials science or image processing (segmentation, smoothing), but they are also beautiful and fascinating in their own right.

Specifically, I have worked on crystal dislocations (a topic related to mean curvature-type evolution equations for curves in a two- or three-dimensional domain) and Willmore's energy (a higher order geometric energy which is frequently used as a model for the bending of thin objects).