5 papers
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…
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…
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…
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…