127 citations · 779 across the 62 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…
A New Riemannian Setting for Surface Registration
Martin Bauer, Martins Bruveris
We present a new approach for matching regular surfaces in a Riemannian setting. We use a Sobolev type metric on deformation vector fields which form the tangent bundle to the spac…
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…