Talk:Geodesics and generalized geodesics

Geodesics in general metric spaces

• Consider either defining L(w), for a general metric space, or linking to a page with the definition.
• ``it is natural to think of Riemannian structure. It can be FORMALLY defined.``
• Remove the ``for p>1``. The fact that geodesics are absolutely continuous curves is true for all p.
• If you would like to include the p in the equation \int_0^1 |c'(t)|^p... you should introduce the W_p metric first.

Statement of Theorem

• Consider changing the name of this section to ``dynamic formulation of Wasserstein distance.
• Remove the requirement p>1; W_1 is also a geodesic space
• Also, there is a small type-o in the continuity equation: it should be the divergence operator \nabla \cdot, instead of the gradient operator \nabla.