Professer

Research interests:

Differential Geometry: I am interested in many areas of differential geometry, including

• geometry of curves, surfaces and hypersurfaces;
• Riemannian geometry;
• effects of local curvature conditions on global geometry and topology;
• geodesics, minimal surfaces, and related problems;
• isoperimetric inequalities;
• differential geometry associated with conformal transformations, projective transformations, affine transformations and other groups;
• general relativity and semi-Riemannian geometry;
• geometry of convex bodies;
• Finsler geometry.

Partial Differential Equations:

• Partial differential equations applied to differential geometry
  • Heat flows applied to prove results in global differential geometry;
    • Moving curves, surfaces and hypersurfaces;
    • Deforming Riemannian metrics or connections;
    • Smoothing effects of heat flows;
  • Minimal surfaces, surfaces of prescribed curvature, and related problems;
  • Harmonic functions and harmonic maps, related variational problems;
• Fully nonlinear elliptic and parabolic equations
  • regularity theory;
  • qualitative and asymptotic behaviour
• Nonlinear wave equations, general relativity;
• Eigenvalue problems arising in geometry;
• Integrable systems arising in geometry.

Applications:

• Tumbling stones and their eventual shapes;
• Image processing;
• Moving interfaces, phase changes, and related problems;
• Reaction-Diffusion systems in mathematical biology;

A list of his publications can be found at http://wwwmaths.anu.edu.au/~andrews/publications.html