32 citations · 135 across the 28 of their papers we have counts for
5 papers · 1 filter
Axisymmetric diffeomorphisms and ideal fluids on Riemannian 3-manifolds
Leandro Lichtenfelz, Gerard Misiolek, Stephen C. Preston
We study the Riemannian geometry of 3D axisymmetric ideal fluids. We prove that the exponential map on the group of volume-preserving diffeomorphisms of a -manifold is Fre…
Shape Analysis of Surfaces Using General Elastic Metrics
Zhe Su, Martin Bauer, Stephen C. Preston +2
In this article we introduce a family of elastic metrics on the space of parametrized surfaces in 3D space using a corresponding family of metrics on the space of vector valued one…
Nonpositive Curvature of the quantomorphism group and quasigeostrophic motion
Jae Min Lee, Stephen C. Preston
In this paper, we compute the sectional curvature of the quantomorphism group whose geodesic equation is the quasi-geostrophic (QG) equation in geophysics and oc…
Isometric Immersions and the Waving of Flags
Martin Bauer, Jakob Møller-Andersen, Stephen C. Preston
In this article we propose a novel geometric model to study the motion of a physical flag. In our approach a flag is viewed as an isometric immersion from the square with values in…
Geodesic completeness of the metric on
Martin Bauer, Boris Kolev, Stephen Preston
Of concern is the study of the long-time existence of solutions to the Euler--Arnold equation of the right-invariant -metric on the diffeomorphism group of the circle. In…