Ben Andrews
BSc PhD ANU
Senior Fellow
Centre for Mathematics and its Applications
Office: Room 2131B, John Dedman Mathematical Sciences Building
Telephone: 6125 3458
Fax: 6125 5549
email:
Ben.Andrews@anu.edu.au
Research
I am a member of the Applied and Nonlinear Analysis Research Group of the Mathematical Sciences Institute.
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;
Personal interests