201 citations · 465 across the 10 of their papers we have counts for
5 papers · 1 filter
Sobolev Metrics on Diffeomorphism Groups and the Derived Geometry of Spaces of Submanifolds
Mario Micheli, Peter W. Michor, David Mumford
Given a finite dimensional manifold , the group of diffeomorphism of which fall suitably rapidly to the identity, acts on the manifold…
Sectional Curvature in terms of the Cometric, with Applications to the Riemannian Manifolds of Landmarks
Mario Micheli, Peter W. Michor, David Mumford
This paper deals with the computation of sectional curvature for the manifolds of landmarks (or feature points) in D dimensions, endowed with the Riemannian metric induced by t…
A Metric on Shape Space with Explicit Geodesics
Peter W. Michor, David Mumford, Jayant Shah +1
This paper studies a specific metric on plane curves that has the property of being isometric to classical manifold (sphere, complex projective, Stiefel, Grassmann) modulo change o…
Vanishing geodesic distance on spaces of submanifolds and diffeomorphisms
Peter W. Michor, David Mumford
The -metric or Fubini-Study metric on the non-linear Grassmannian of all submanifolds of type in a Riemannian manifold induces geodesic distance 0. We discuss anot…
Riemannian geometries on spaces of plane curves
Peter W. Michor, David Mumford
We study some Riemannian metrics on the space of regular smooth curves in the plane, viewed as the orbit space of maps from to the plane modulo the group of diffeomorphisms o…