View source for Geodesics and generalized geodesics

== Introduction ==

There are many ways that we can characterize [https://en.wikipedia.org/wiki/ Wasserstein metric] ... [http://34.106.105.83/wiki/Formal_Riemannian_Structure_of_the_Wasserstein_metric]

The main idea is to characterize absolutely (AC) curves ...

== Statement of Theorem==

: '''Theorem.'''(Benamow-Brenier)<ref name=Santambrogio /> Let <math> \mu, \nu \in P_{2}(R^{d}) </math>, <br>
<math> W_{2}^{2}(\mu, \nu)=\inf_{(\mu(t).\nu(t))} \{\int_{0}^{1} |v(,t)|_{L^{2}(\mu(t))}^{2}dt, \quad \partial_{t}\mu+\nabla(v\mu)=0, \mu(0)=\mu, \mu(1)=\nu \} </math>

== Generalization ==

= References =

<references>

<ref name="Santambrogio"> [https://link-springer-com.proxy.library.ucsb.edu:9443/book/10.1007/978-3-319-20828-2 F. Santambrogio, ''Optimal Transport for Applied Mathematicians'', Chapter 1, pages 9-16] </ref>

</references>