79 citations · 638 across the 61 of their papers we have counts for
11 papers · 1 filter
Madelung hydrodynamics and Poisson geometry of wave functions
Boris Khesin, Klas Modin
We describe the Poisson geometry of the Madelung transform between quantum mechanics and hydrodynamics for generic wave functions. We prove that for arbitrary oriented manifolds th…
Universal vector and matrix optimal transport
Boris Khesin, Klas Modin
In this paper we propose a gauge-theoretic approach to the problems of optimal mass transport for vector and matrix densities. This resolves both the issues of positivity and actio…
Ricci curvature for hydrodynamics on the sphere
Leandro Lichtenfelz, Klas Modin, Stephen C. Preston
The geometric description of incompressible hydrodynamics, as geodesic motion on the infinite-dimensional group of volume-preserving diffeomorphisms, enables notions of curvature i…
Information geometry of diffeomorphism groups
Boris Khesin, Gerard Misiołek, Klas Modin
The study of diffeomorphism groups and their applications to problems in analysis and geometry has a long history. In geometric hydrodynamics, pioneered by V.~Arnold in the 1960s,…
Zeitlin's model for axisymmetric 3-D Euler equations
Klas Modin, Stephen C. Preston
Zeitlin's model is a spatial discretization for the 2-D Euler equations on the flat 2-torus or the 2-sphere. Contrary to other discretizations, it preserves the underlying geometri…
Simple unbalanced optimal transport
Boris Khesin, Klas Modin, Luke Volk
We introduce and study a simple model capturing the main features of unbalanced optimal transport. It is based on equipping the conical extension of the group of all diffeomorphism…