I have been working mainly on geometric flows. More generally, I study nonlinear partial differential equations, with an emphasis on those arising in the calculus of variations, geometric analysis, applied analysis and differential geometry.
Particular areas of specialisation currently include
1) Harmonic maps and their heat flow; bubbling phenomena.
2) Ricci flow.
3) Compensation properties of Jacobian determinants
4) Isoperimetric inequalities.
5) Minimal surfaces and mean curvature flow.
6) Willmore surfaces.
7) Fluid dynamics.