145 citations · 1.3k across the 104 of their papers we have counts for
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Geodesic Completeness for Sobolev Metrics on the Space of Immersed Plane Curves
Martins Bruveris, Peter W. Michor, David Mumford
We study properties of Sobolev-type metrics on the space of immersed plane curves. We show that the geodesic equation for Sobolev-type metrics with constant coefficients of order 2…
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…
Vanishing geodesic distance for the Riemannian metric with geodesic equation the KdV-equation
Martin Bauer, Martins Bruveris, Philipp Harms +1
The Virasoro-Bott group endowed with the right-invariant -metric (which is a weak Riemannian metric) has the KdV-equation as geodesic equation. We prove that this metric space…
Some Geometric Evolution Equations Arising as Geodesic Equations on Groups of Diffeomorphisms Including the Hamiltonian Approach
Peter W. Michor
This is the extended version of a lecture course given at the University of Vienna in the spring term 2005. The main aim of this course was to understand the papers \cite{10} and \…
Bounds on the multiplicity of eigenvalues for fixed membranes
Thomas Hoffman-Ostenhof, Peter W. Michor, Nikolai Nadirashvili
For a membrane in the plane the multiplicity of the -th eigenvalue is known to be not greater than . Here we prove that it is actually not greater than , for $k\ge 3…