Asymptotic directions, Monge-Ampere equations and the geometry of diffeomorphism groups
Khesin, Boris ; Misiolek, Gerard
arXiv, 0504556 / Harvested from arXiv
Text on arXiv
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.
Publié le : 2005-04-27
Classification:  Mathematics - Differential Geometry,  Mathematical Physics,  58B20 (Primary),  76B03 (Secondary) 
@article{0504556,
     author = {Khesin, Boris and Misiolek, Gerard},
     title = {Asymptotic directions, Monge-Ampere equations and the geometry of
  diffeomorphism groups},
     journal = {arXiv},
     volume = {2005},
     number = {0},
     year = {2005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0504556}
}

Khesin, Boris; Misiolek, Gerard. Asymptotic directions, Monge-Ampere equations and the geometry of
  diffeomorphism groups. arXiv, Tome 2005 (2005) no. 0, . http://gdmltest.u-ga.fr/item/0504556/