Completeness and Geodesic Distance Properties for Fractional Sobolev Metrics on Spaces of Immersed Curves

DOI10.1007/S12220-024-01652-3MaRDI QIDQ6500228

Cy Maor, Martin Bauer, Unnamed Author

Publication date: 10 May 2024

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

Existence problems for PDEs: global existence, local existence, non-existence (35A01) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Initial value problems for systems of nonlinear higher-order PDEs (35G55)

Cites Work

Unnamed Item
Unnamed Item
The SQG equation as a geodesic equation
Functional and shape data analysis
Sobolev metrics on shape space of surfaces
Hitchhiker's guide to the fractional Sobolev spaces
A discrete transform and decompositions of distribution spaces
Vanishing geodesic distance for the Riemannian metric with geodesic equation the KdV-equation
Geometric investigations of a vorticity model equation
Completeness properties of Sobolev metrics on the space of curves
Wave breaking for nonlinear nonlocal shallow water equations
Euler-Arnold equations and Teichmüller theory
Fractional Sobolev metrics on spaces of immersed curves
Half-Lie groups
The geometry of a vorticity model equation
Regularity of maps between Sobolev spaces
Sobolev gradients for the Möbius energy
Geodesic completeness of the \(H^{3/2}\) metric on \(\text{Diff}(S^1)\)
Geodesic distance for right-invariant metrics on diffeomorphism groups: critical Sobolev exponents
Geodesic distance for right invariant Sobolev metrics of fractional order on the diffeomorphism group
Riemannian geometries on spaces of plane curves
Overview of the geometries of shape spaces and diffeomorphism groups
Right-invariant Sobolev metrics of fractional order on the diffeomorphism group of the circle
Groups of diffeomorphisms and the motion of an incompressible fluid
Vanishing geodesic distance on spaces of submanifolds and diffeomorphisms
On completeness of groups of diffeomorphisms
GEODESIC COMPLETENESS FOR SOBOLEV METRICS ON THE SPACE OF IMMERSED PLANE CURVES
On the Geodesic Flow on the Group of Diffeomorphisms of the Circle with a Fractional Sobolev Right-Invariant Metric
The Hopf-Rinow Theorem is false in infinite Dimensions
BIINVARIANT METRICS ON THE GROUP OF HAMILTONIAN DIFFEOMORPHISMS
On the geometric approach to the motion of inertial mechanical systems
An integrable shallow water equation with peaked solitons
A First Course in Sobolev Spaces
Topological Methods in Hydrodynamics
A remark on vanishing geodesic distances in infinite dimensions
Hilbert Manifolds Without Epiconjugate Points
A First Course in Fractional Sobolev Spaces
Shapes and diffeomorphisms
On the \(H^1 (ds^{\gamma})\)-gradient flow for the length functional
A speed preserving Hilbert gradient flow for generalized integral Menger curvature

This page was built for publication: Completeness and Geodesic Distance Properties for Fractional Sobolev Metrics on Spaces of Immersed Curves