Completeness properties of Sobolev metrics on the space of curves

DOI10.3934/jgm.2015.7.125zbMath1328.58007arXiv1407.0601OpenAlexW1792347967MaRDI QIDQ888755

Martins Bruveris

Publication date: 2 November 2015

Published in: Journal of Geometric Mechanics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1407.0601

zbMATH Keywords

completenessshape spaceminimizing geodesicsSobolev metricsimmersed curves

Mathematics Subject Classification ID

Spaces of embeddings and immersions (58D10) Riemannian, Finsler and other geometric structures on infinite-dimensional manifolds (58B20) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Curves in Euclidean and related spaces (53A04)

Related Items

Optimal Reparametrizations in the Square Root Velocity Framework, A New Variational Model for Shape Graph Registration with Partial Matching Constraints, Designing metrics; the delta metric for curves, A relaxed approach for curve matching with elastic metrics, Mathematical imaging and surface processing. Abstracts from the workshop held August 21--27, 2022, HV geometry for signal comparison, Fractional Sobolev metrics on spaces of immersed curves, Variational Methods for Discrete Geometric Functionals, Manifolds of Mappings for Continuum Mechanics, Regularity of maps between Sobolev spaces, Why Use Sobolev Metrics on the Space of Curves, A numerical framework for elastic surface matching, comparison, and interpolation, Elastic energy regularization for inverse obstacle scattering problems, A Numerical Framework for Sobolev Metrics on the Space of Curves

Uses Software

• DLMF

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Sobolev metrics on the manifold of all Riemannian metrics
• An \(H^2\) Riemannian metric on the space of planar curves modulo similitudes
• Sobolev metrics on shape space of surfaces
• Metrics on spaces of immersions where horizontality equals normality
• Vanishing geodesic distance for the Riemannian metric with geodesic equation the KdV-equation
• Generalized gradients: priors on minimization flows
• A metric on shape space with explicit geodesics
• Diffeomorphism groups of compact manifolds
• Properties of Sobolev-type metrics in the space of curves
• Riemannian exponential maps of the diffeomorphism group of \(\mathbb T^2\)
• Inequalities for differential and integral equations
• The action of the diffeomorphism group on the space of immersions
• Sobolev metrics on shape space. II: Weighted Sobolev metrics and almost local metrics
• \(R\)-transforms for Sobolev \(H^2\)-metrics on spaces of plane curves
• An overview of the Riemannian metrics on spaces of curves using the Hamiltonian approach
• Constructing reparameterization invariant metrics on spaces of plane curves
• Riemannian geometries on spaces of plane curves
• The homotopy type of the space of degree 0 -- inmersed plane curves
• Overview of the geometries of shape spaces and diffeomorphism groups
• Groups of diffeomorphisms and the motion of an incompressible fluid
• Vanishing geodesic distance on spaces of submanifolds and diffeomorphisms
• GEODESIC COMPLETENESS FOR SOBOLEV METRICS ON THE SPACE OF IMMERSED PLANE CURVES
• Variational time discretization of geodesic calculus
• $H^{o}$-type Riemannian metrics on the space of planar curves
• The inverse function theorem of Nash and Moser
• The Camassa–Holm equation as a geodesic flow on the diffeomorphism group
• On the regularity of the composition of diffeomorphisms
• Variational, Geometric, and Level Set Methods in Computer Vision
• Fundamental Inequalities for Discrete and Discontinuous Functional Equations
• On the space of Riemannian metrics
• Condition $\left( {\text{C}} \right)$ and geodesics on Sobolev manifolds
• Riemannian geometry.