5 citations · 7 across the 4 of their papers we have counts for
5 papers
Singular Sets of Riemannian Exponential Maps in Hydrodynamics
James Benn, Patrick Heslin, Leandro Lichtenfelz +1
We prove that the singular sets for the Lagrangian solution maps of the two-dimensional inviscid Euler and generalized surface quasi-geostrophic equations are Gaussian null sets. T…
Principal subbundles for dimension reduction
Morten Akhøj, James Benn, Erlend Grong +2
In this paper we demonstrate how sub-Riemannian geometry can be used for manifold learning and surface reconstruction by combining local linear approximations of a point cloud to o…
Sobolev Geometry of the Symplectomorphism Group
James Benn, Ali Suri
For a closed symplectic manifold with compatible Riemannian metric we study the Sobolev geometry of the group of all diffeomorphisms on which preserve t…
Currents and finite elements as tools for shape space
James Benn, Stephen Marsland, Robert I McLachlan +2
The nonlinear spaces of shapes (unparameterized immersed curves or submanifolds) are of interest for many applications in image analysis, such as the identification of shapes that…
The exponential map of the group of area-preserving diffeomorphisms of a surface with boundary
James Benn, Gerard Misiolek, Stephen C. Preston
We prove that the Riemannian exponential map of the right-invariant metric on the group of volume-preserving diffeomorphisms of a two-dimensional manifold with a nonempty bou…