Sobolev metrics on diffeomorphism groups and the derived geometry of spaces of submanifolds

DOI10.1070/IM2013v077n03ABEH002648zbMath1280.58005arXiv1202.3677WikidataQ62597155 ScholiaQ62597155MaRDI QIDQ5327397

Mario Micheli, Peter W. Michor, David Mumford

Publication date: 7 August 2013

Published in: Izvestiya: Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1202.3677

zbMATH Keywords

curvature in terms of the cometricmanifold of submanifoldsO'Neill's formularight-invariant Sobolev metrics on diffeomorphism groupsrobust infinite-dimensional weak Riemannian manifolds

Mathematics Subject Classification ID

Riemannian, Finsler and other geometric structures on infinite-dimensional manifolds (58B20) Hamiltonian systems on groups of diffeomorphisms and on manifolds of mappings and metrics (37K65) Manifolds of mappings (58D15)

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Cites Work

• Homogeneous Sobolev metric of order one on diffeomorphism groups on real line
• A metric on shape space with explicit geodesics
• An overview of the Riemannian metrics on spaces of curves using the Hamiltonian approach
• Riemannian geometries on spaces of plane curves
• 2D-shape analysis using conformal mapping
• Sur la géométrie différentielle des groupes de Lie de dimension infinite et ses applications à l'hydrodynamique des fluides parfaits
• Sectional Curvature in Terms of the Cometric, with Applications to the Riemannian Manifolds of Landmarks
• Teichons: Solitonlike Geodesics on Universal Teichmüller Space
• Diffeomorphic Surface Flows: A Novel Method of Surface Evolution
• Shapes and diffeomorphisms
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