Mesh adaptation on the sphere using optimal transport and the numerical solution of a Monge-Ampère type equation

- Numerical solution of the Monge-Ampère equation on the surface of a sphere.
- Optimal transport for mesh adaptation.
- New linearisation of the Monge-Ampère equation and exponential maps.
- Proof of existence of solutions.
- Comparisons with centroidal Voronoi tessellations on the sphere.