My research focuses on submanifold geometry in symmetric spaces, and on mean curvature flow and inverse mean curvature flow — geometric flows closely related to the Ricci flow used in the resolution of the Poincaré conjecture. I am also interested in connections with general relativity and gauge theory.
Reduction to the study of submanifolds in an infinite-dimensional Hilbert space via a Riemannian submersion, exploiting the flatness and absolute parallelism of the Hilbert space.
Reduction via complexification (anti-Kaehler submanifolds) to the study of submanifolds in an infinite-dimensional anti-Kaehler space.
Collapse, divergence and convergence behaviour of submanifolds evolving under (modified) mean curvature flow equations.
Defining mean curvature flow with surgery for certain hypersurfaces and applying it to study their topology.