Skip to content

Integrable Systems and Surface Geometry

This is the central line of my research. It concerns the appearance of integrable systems in surface theory through moving frames, loop groups, flat connections, and the DPW method.

Topics

  • Constant mean curvature surfaces in space forms.
  • Constant Gaussian curvature surfaces.
  • Minimal surfaces in homogeneous three-manifolds.
  • Harmonic maps and loop group methods.
  • Real forms of complex surface theories.

Representative publications

  • Constant mean curvature surfaces in hyperbolic 3-space via loop groups.
  • Real forms of complex surfaces of constant mean curvature.
  • Minimal cylinders in the three-dimensional Heisenberg group.
  • A duality for minimal surfaces in the Heisenberg group.