145 citations · 1.3k across the 104 of their papers we have counts for
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Determination of all diffeomorphism invariant tensor fields on the space of smooth positive densities on a compact manifold with corners
Peter W. Michor
It was proved in [3] that on a closed manifold of dimension greater than one, every smooth weak Riemannian metric on the space of smooth positive probability densities, that is inv…
The Wasserstein--Ebin Metric: A Geometric Lift of Unbalanced Optimal Transport to the space of Riemannian metrics
Martin Bauer, Peter W. Michor, François-Xavier Vialard
We introduce dynamic and static formulations that formally extend unbalanced optimal transport from the space of positive densities to the space of Riemannian metrics. The first co…
The Schouten-Nijenhuis bracket in infinite dimensions
Peter W. Michor
The Schouten-Nijenhuis bracket on smooth infinite-dimensional manifolds is developed in two steps: For summable multivector fields whose pointwise dual are all differential for…
Geometry of infinite dimensional Cartan Developments
Johanna Michor, Peter W. Michor
The Cartan development takes a Lie algebra valued 1-form satisfying the Maurer-Cartan equation on a simply connected manifold to a smooth mapping from into the Lie group. I…
Regularity and completeness of half-Lie groups
Martin Bauer, Philipp Harms, Peter W. Michor
Half Lie groups exist only in infinite dimensions: They are smooth manifolds and topological groups such that right translations are smooth, but left translations are merely requir…
Orbifold-like and proper -manifolds
Franz W. Kamber, Peter W. Michor
In [4] and [5], we generalized the concept of completion of an infinitesimal group action to an actual group action on a (non-compact) manifo…