Ben Andrews

Contacts
Contact email:Ben.Andrews@anu.edu.au
Contact phone:+61 2 6125 3458
Location:Room 3.72, Hanna Neumann Building 145
Professor
Read more about Ben's biography and research interests.
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.
Groups
- Convenor, Applied & nonlinear analysis
Projects
- Supervisor, Curve shortening flow
- Supervisor, Eigenvalues of the Laplacian on Riemannian manifolds
- Supervisor, Minimal surfaces in the sphere