# Professor Ben Andrews

## Profile

### Biography

Read more about Ben's biography and research interests here.

## Research

### 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.