Asymptotic directions, Monge-Ampere equations and the geometry of diffeomorphism groups
Differential Geometry
2007-05-23 v1 Mathematical Physics
math.MP
Abstract
In this note we obtain the characterization for asymptotic directions on various subgroups of the diffeomorphism group. We give a simple proof of non-existence of such directions for area-preserving diffeomorphisms of closed surfaces of non-zero curvature. Finally, we exhibit the common origin of the Monge-Ampere equations in 2D fluid dynamics and mass transport.
Keywords
Cite
@article{arxiv.math/0504556,
title = {Asymptotic directions, Monge-Ampere equations and the geometry of diffeomorphism groups},
author = {Boris Khesin and Gerard Misiolek},
journal= {arXiv preprint arXiv:math/0504556},
year = {2007}
}
Comments
10 pages, 1 fig., to appear in J. of Math. Fluid Mechanics