32 citations · 135 across the 28 of their papers we have counts for
4 papers · 1 filter
Curvatures of Sobolev metrics on diffeomorphism groups
Boris Khesin, Jonatan Lenells, Gerard Misiolek +1
Many conservative partial differential equations correspond to geodesic equations on groups of diffeomorphisms. Stability of their solutions can be studied by examining sectional c…
The motion of whips and chains
Stephen C. Preston
We study the motion of an inextensible string (a whip) fixed at one point in the absence of gravity, satisfying the equations $$ η_{tt} = \partial_s(ση_s), \qquad σ_{ss}-\lvert η_{…
The geometry of whips
Stephen C. Preston
In this paper we study geometric aspects of the space of arcs parametrized by unit speed in the metric. Physically this corresponds to the motion of a whip, and it also arise…
Geometry of diffeomorphism groups, complete integrability and optimal transport
Boris Khesin, Jonatan Lenells, Gerard Misiolek +1
We study the geometry of the space of densities $\VolM$, which is the quotient space $\Diff(M)/\Diff_μ(M)$ of the diffeomorphism group of a compact manifold by the subgroup of…