145 citations · 1.3k across the 104 of their papers we have counts for
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The Lagrangian Radon Transform and the Weil representation
Giuseppe Marmo, Peter W. Michor, Yuri Neretin
We consider the operator , which sends a function on to its integrals over all affine Lagrangian subspaces in . We discuss properties o…
Geodesic distance for right invariant Sobolev metrics of fractional order on the diffeomorphism group. II
Martin Bauer, Martins Bruveris, Peter W. Michor
The geodesic distance vanishes on the group of compactly supported diffeomorphisms of a Riemannian manifold of bounded geometry, for the right invariant weak Riemannian metric…
Sobolev metrics on shape space of surfaces
Philipp Harms
Many procedures in science, engineering and medicine produce data in the form of geometric shapes. Mathematically, a shape can be modeled as an un-parameterized immersed sub-manifo…
A zoo of diffeomorphism groups on
Peter W. Michor, David Mumford
We consider the groups , , and of smooth…
The homogeneous Sobolev metric of order one on diffeomorphism groups on the real line
Martin Bauer, Martins Bruveris, Peter W. Michor
In this article we study Sobolev metrics of order one on diffeomorphism groups on the real line. We prove that the space equipped with the homo…
Constructing reparametrization invariant metrics on spaces of plane curves
Martin Bauer, Martins Bruveris, Stephen Marsland +1
Metrics on shape space are used to describe deformations that take one shape to another, and to determine a distance between them. We study a family of metrics on the space of curv…