Ben Andrews

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

Supervised students