A zoo of diffeomorphism groups on \(\mathbb R^n\)

DOI10.1007/s10455-013-9380-2zbMath1364.22009arXiv1211.5704OpenAlexW3123533845WikidataQ56041907 ScholiaQ56041907MaRDI QIDQ2434951

David Mumford, Peter W. Michor

Publication date: 3 February 2014

Published in: Annals of Global Analysis and Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1211.5704

zbMATH Keywords

diffeomorphism groupconvenient calculusinfinite dimensional regular Lie group

Mathematics Subject Classification ID

Infinite-dimensional Lie groups and their Lie algebras: general properties (22E65)

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Cites Work

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• On Euler's equation and `EPDiff'
• Homogeneous Sobolev metric of order one on diffeomorphism groups on real line
• On regular Frechet-Lie groups. V: Several basic properties
• Vanishing geodesic distance for the Riemannian metric with geodesic equation the KdV-equation
• On regular Frechet-Lie groups. IV: Definition and fundamental theorems
• Geodesic distance for right invariant Sobolev metrics of fractional order on the diffeomorphism group
• Geodesic distance for right invariant Sobolev metrics of fractional order on the diffeomorphism group. II
• Weighted diffeomorphism groups of Banach spaces and weighted mapping groups
• Sobolev metrics on diffeomorphism groups and the derived geometry of spaces of submanifolds

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