32 citations · 135 across the 28 of their papers we have counts for
23 papers · 1 filter
Characterization of geodesic completeness for landmark space
Karen Habermann, Stephen C. Preston, Stefan Sommer
We provide a full characterization of geodesic completeness for spaces of configurations of landmarks with smooth Riemannian metrics that satisfy a rotational and translation invar…
Conjugate points along Kolmogorov flows on the torus
Alice Le Brigant, Stephen C. Preston
The geodesics in the group of volume-preserving diffeomorphisms (volumorphisms) of a manifold , for a Riemannian metric defined by the kinetic energy, can be used to model the m…
3 methods to put a Riemannian metric on Shape Space
Alice Barbora Tumpach, Stephen C. Preston
In many applications, one is interested in the shape of an object, like the contour of a bone or the trajectory of joints of a tennis player, irrespective of the way these shapes a…
Conjugate point criteria on the area-preserving diffeomorphism group
Stephen C. Preston
This paper answers some questions about conjugate points along the geodesics corresponding to steady 2D Euler flows, posed by a paper of Drivas-Misiolek-Shi-Yoneda. We present a ne…
Fisher-Rao geometry of Dirichlet distributions
Alice Le Brigant, Stephen Preston, Stéphane Puechmorel
In this paper, we study the geometry induced by the Fisher-Rao metric on the parameter space of Dirichlet distributions. We show that this space is geodesically complete and has ev…
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…