Curvature weighted metrics on shape space of hypersurfaces in n-space

CURVATURE WEIGHTED METRICS ON SHAPE SPACE OF HYPERSURFACES IN n-SPACE

Let M be a compact connected oriented n−1 dimensional manifold without boundary. In this work, shape space is the orbifold of unparametrized immersions from M to Rn. The results of [1], where mean curvature weighted metrics were studied, suggest to incorporate Gauß curvature weights in the definition of the metric. This leads us to study metrics on shape space that are induced by metrics on the...

Sobolev Metrics on Shape Space of Hypersurfaces in N-space

This paper extends parts of the results from [10] for plane curves to the case of hypersurfaces in R. Let M be a compact connected oriented n − 1 dimensional manifold without boundary. Then shape space is either the manifold of submanifolds of R of type M , or the orbifold of immersions from M to R modulo the group of diffeomorphisms of M . We investigate the Sobolev Riemannian metrics on shape...

Almost Local Metrics on Shape Space of Hypersurfaces in n-Space

This paper extends parts of the results from [17] for plane curves to the case of hypersurfaces in Rn. Let M be a compact connected oriented n − 1 dimensional manifold without boundary like S2 or the torus S1 × S1. Then shape space is either the manifold of submanifolds of Rn of type M , or the orbifold of immersions from M to Rn modulo the group of diffeomorphisms of M . We investigate almost ...

Hypersurfaces with Constant Mean Curvature in a Lorentzian Space Form

Sobolev Metrics on Shape Space of Surfaces in N-space

This paper extends parts of the results from [14] for plane curves to the case of surfaces in Rn. Let M be a compact connected oriented manifold of dimension less than n without boundary. Then shape space is either the manifold of submanifolds of Rn of type M , or the orbifold of immersions from M to Rn modulo the group of diffeomorphisms of M . We investigate the Sobolev Riemannian metrics on ...