A McLean Theorem for the moduli space of Lie solutions to mass transport equations

Details A McLean Theorem for the moduli space of Lie solutions to mass transport equations A McLean Theorem for the moduli space of Lie solutions to mass transport equations

2010-06-07

arxiv.org/abs/1006.1334v3

Mathematics

Differential Geometry

cleaned up a little from previous version

Scientific paper

On compact manifolds which are not simply connected, we prove the existence of "fake" solutions to the optimal transportion problem. These maps preserve volume and arise as the exponential of a closed 1 form, hence appear geometrically like optimal transport maps. The set of such solutions forms a manifold with dimension given by the first Betti number of the manifold. In the process, we prove a Hodge-Helmholtz decomposition for vector fields. The ideas are motivated by the analogies between special Lagrangian submanifolds and solutions to optimal transport problems.

Affiliated with

Also associated with

No associations

Rating

A McLean Theorem for the moduli space of Lie solutions to mass transport equations does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A McLean Theorem for the moduli space of Lie solutions to mass transport equations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A McLean Theorem for the moduli space of Lie solutions to mass transport equations will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-367864