3 papers
math.DG2025
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…
stat.ME2023
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…
math.DG2017
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…