81 citations · 344 across the 24 of their papers we have counts for
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Sobolev Metrics on Shape Space, II: Weighted Sobolev Metrics and Almost Local Metrics
Martin Bauer, Philipp Harms, Peter W. Michor
In continuation of [3] we discuss metrics of the form $$ G^P_f(h,k)=\int_M \sum_{i=0}^pΦ_i(\Vol(f)) \g((P_i)_fh,k) \vol(f^*\g) $$ on the space of immersions $\Imm(M,N)$ and on shap…
Geodesic distance for right invariant Sobolev metrics of fractional order on the diffeomorphism group
Martin Bauer, Martins Bruveris, Philipp Harms +1
We study Sobolev-type metrics of fractional order on the group $\Diff_c(M)$ of compactly supported diffeomorphisms of a manifold . We show that for the important specia…
Curvature weighted metrics on shape space of hypersurfaces in -space
Martin Bauer, Philipp Harms, Peter W. Michor
Let be a compact connected oriented dimensional manifold without boundary. In this work, shape space is the orbifold of unparametrized immersions from to $\mathbb R^n…
Sobolev metrics on the manifold of all Riemannian metrics
Martin Bauer, Philipp Harms, Peter W. Michor
On the manifold $\Met(M)$ of all Riemannian metrics on a compact manifold one can consider the natural -metric as described first by \cite{Ebin70}. In this paper we consid…
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…