Geodesic distance for right invariant Sobolev metrics of fractional order on the diffeomorphism group. II

DOI10.1007/s10455-013-9370-4zbMath1290.35192arXiv1212.4610OpenAlexW2050273278WikidataQ62597151 ScholiaQ62597151MaRDI QIDQ2434957

Martins Bruveris, Martin Bauer, 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/1211.7254

zbMATH Keywords

Riemannian manifolddiffeomorphism groupgeodesic distanceSobolev metrics of non-integral order

Mathematics Subject Classification ID

Riemannian, Finsler and other geometric structures on infinite-dimensional manifolds (58B20) Euler equations (35Q31)

Related Items (11)

Geometric investigations of a vorticity model equation ⋮ Vanishing geodesic distance for right-invariant Sobolev metrics on diffeomorphism groups ⋮ On the Michor-Mumford phenomenon in the infinite dimensional Heisenberg group ⋮ A zoo of diffeomorphism groups on \(\mathbb R^n\) ⋮ Manifolds of Mappings for Continuum Mechanics ⋮ Can we run to infinity? The diameter of the diffeomorphism group with respect to right-invariant Sobolev metrics ⋮ Local and global well-posedness of the fractional order EPDiff equation on \(\mathbb{R}^d\) ⋮ Overview of the geometries of shape spaces and diffeomorphism groups ⋮ Why Use Sobolev Metrics on the Space of Curves ⋮ Vanishing distance phenomena and the geometric approach to SQG ⋮ Geodesic distance for right-invariant metrics on diffeomorphism groups: critical Sobolev exponents

Uses Software

• DLMF

Cites Work

• Vanishing geodesic distance for the Riemannian metric with geodesic equation the KdV-equation
• \(L^ p\)-theory of elliptic differential operators on manifolds of bounded geometry
• Complete metrics of bounded curvature on noncompact manifolds
• Commutators of diffeomorphisms
• Geodesic distance for right invariant Sobolev metrics of fractional order on the diffeomorphism group
• A zoo of diffeomorphism groups on \(\mathbb R^n\)
• The Boundedness of Connection Coefficients and their Derivatives
• Foliations and groups of diffeomorphisms
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