Talk:Geodesics and generalized geodesics: Difference between revisions
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==Geodesics in general metric spaces== | ==Geodesics in general metric spaces== | ||
* Consider either defining L(w), for a general metric space, or linking to a page with the definition. | * 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. | * ``it is natural to think of Riemannian structure. It can be FORMALLY defined.`` | ||
* Remove the ``for p>1 | * 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. | * 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== | ==Statement of Theorem== | ||
Latest revision as of 03:59, 12 June 2020
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.