Ben Andrews
BSc PhD ANU
Fellow of the Australian Academy of Science
Fellow of the American Mathematical Society
Fellow of the Australian Mathematical Society
Professor and ARC Laureate 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