Doing a course on Mathematical Relativity (never had a true Relativity course before) this semester, where I have to do a project on a topic not in the programme. I already did courses on Riemannian Geometry and Geometric Mechanics.
I would like to know beforehand if there are any interesting applications of Calculus of Variations or Geometric Analysis (like minimal surfaces, ect) to pursue. Nothing really complicated as the project itself does not need to be original, yet nothing so trivial as to induce boredom.
Thank you for your time!
Read this paper and hope you will learn a lot along the way.
http://www.math.toronto.edu/mccann/papers/GRO.pdf