Teichmüller Theory and Harmonic Maps

This theme studies geometric structures related to harmonic maps, Teichmüller theory, and the complex landslide flow. It develops integrable-systems methods as a tool for studying geometric deformation problems.

Topics

• Complex landslide flow.
• Harmonic maps into hyperbolic two-space.
• Constant Gaussian curvature surfaces in hyperbolic three-space.
• Connections with Teichmüller theory and geometric transitions.

Representative publications

• The complex landslide flow and the method of integrable systems.
• A classification of constant Gaussian curvature surfaces in the three-dimensional hyperbolic space.