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math.DG2025
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…
math.DG2025
Geodesic interpretation of the global quasi-geostrophic equations
Klas Modin, Ali Suri
We give an interpretation of the global shallow water quasi-geostrophic equations on the sphere $\Sph^2$ as a geodesic equation on the central extension of the quantomorphism group…
math.DG2024★ 1 cited
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,…