145 citations · 1.3k across the 104 of their papers we have counts for
109 papers
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…
Landmark shape spaces with induced metrics
Sarang Joshi, Peter W. Michor, Stefan Sommer
We present a unification of Kendall's landmark shape spaces, where rigid motions are factored out and scale fixed on landmark configurations equipped with Euclidean geometry, with…
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…
Symplectic structures on the space of space curves
Martin Bauer, Sadashige Ishida, Peter W. Michor
We present symplectic structures on the shape space of unparameterized space curves that generalize the classical Marsden-Weinstein structure. Our method integrates the Liouville 1…
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…