32 citations · 135 across the 28 of their papers we have counts for
33 papers
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…
Liouville comparison theory for blowup of Euler-Arnold equations
Martin Bauer, Stephen C. Preston, Justin Valletta
In this article we introduce a new blowup criterion for (generalized) Euler-Arnold equations on . Our method is based on treating the equation in Lagrangian coordinate…
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…
Solar models and McKean's breakdown theorem for the CH and DP equations
Stephen C. Preston
We study the breakdown for CH and DP equations on the circle, given by for , where is the mean and or respect…