{"paper":{"title":"Almost local metrics on shape space of hypersurfaces in n-space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Martin Bauer, Peter W. Michor, Philipp Harms","submitted_at":"2010-01-05T15:08:15Z","abstract_excerpt":"This paper extends parts of the results from [P.W.Michor and D. Mumford, \\emph{Appl. Comput. Harmon. Anal.,} 23 (2007), pp. 74--113] for plane curves to the case of hypersurfaces in $\\mathbb R^n$. Let $M$ be a compact connected oriented $n-1$ dimensional manifold without boundary like the sphere or the torus. Then shape space is either the manifold of submanifolds of $\\mathbb R^n$ of type $M$, or the orbifold of immersions from $M$ to $\\mathbb R^n$ modulo the group of diffeomorphisms of $M$. We investigate almost local Riemannian metrics on shape space. These are induced by metrics of the foll"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1001.0717","kind":"arxiv","version":5},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}