Harmonic analysis meets critical knots. Critical points of the Möbius energy are smooth

DOI10.1090/tran/6603zbMath1335.49074arXiv1202.5426OpenAlexW3106086978MaRDI QIDQ2790734

Philipp Reiter, Armin Schikorra, Simon Blatt

Publication date: 8 March 2016

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1202.5426

zbMATH Keywords

Euler-Lagrange equationsfractional Sobolev spacesfractional Laplacianfractional harmonic mapsMöbius energycharged curvecritical knots

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Variational problems in a geometric measure-theoretic setting (49Q20) Regularity of solutions in optimal control (49N60)

Related Items

On the analyticity of critical points of the Möbius energy, On the analyticity of critical points of the generalized integral Menger curvature in the Hilbert case, Nonlinear commutators for the fractional \(p\)-Laplacian and applications, On a new class of fractional partial differential equations. II, A fractional version of Rivière's \(\mathrm{GL(n)}\)-gauge, On energy-critical half-wave maps into \(\mathbb {S}^2\), On some knot energies involving Menger curvature, On regularity theory for \(n/p\)-harmonic maps into manifolds, Residues of manifolds, Blow-up behavior of a fractional Adams–Moser–Trudinger-type inequality in odd dimension, Regularity for a fractional p-Laplace equation, Möbius-invariant self-avoidance energies for non-smooth sets of arbitrary dimension and co-dimension, A fractional Korn-type inequality, Minimal Ws,ns$W^{s,\frac{n}{s}}$‐harmonic maps in homotopy classes, Dynamics of embedded curves by doubly-nonlocal reaction–diffusion systems, Variational formulae and estimates of O’Hara’s knot energies, Möbius invariant metrics on the space of knots, Sharp commutator estimates via harmonic extensions, Fractional div-curl quantities and applications to nonlocal geometric equations, The elastic trefoil is the doubly covered circle, Three examples of sharp commutator estimates via harmonic extensions, Boundary equations and regularity theory for geometric variational systems with Neumann data, \(\varepsilon\)-regularity for systems involving non-local, antisymmetric operators, Limits of conformal immersions under a bound on a fractional normal curvature quantity, Decomposition of generalized O'Hara's energies, Upper and lower bounds and modulus of continuity of decomposed Möbius energies, Regularization of Neumann and Weber formulae for inductance, Sobolev gradients for the Möbius energy, Elastic energy regularization for inverse obstacle scattering problems, On O'Hara knot energies. I: Regularity for critical knots, Curves between Lipschitz and \(C^1\) and their relation to geometric knot theory, On the regularity of critical points for O’Hara’s knot energies: From smoothness to analyticity

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Fractional harmonic maps into manifolds in odd dimension \(n > 1\)
• Hitchhiker's guide to the fractional Sobolev spaces
• Sub-criticality of non-local Schrödinger systems with antisymmetric potentials and applications to half-harmonic maps
• Regularity theory for the Möbius energy
• Three-term commutator estimates and the regularity of \(^{1}/_{2}\)-harmonic maps into spheres
• Regularity of \(n/2\)-harmonic maps into spheres
• The gradient flow of the Möbius energy near local minimizers
• Energy of a knot
• An introduction to Sobolev spaces and interpolation spaces
• Analysis aspects of Willmore surfaces
• Theory of function spaces
• A note on Riesz potentials
• A formula for the non-integer powers of the Laplacian
• Energy functionals of knots. II
• Möbius energy of knots and unknots
• Existence of surfaces minimizing the Willmore functional
• Stationary points of O'Hara's knot energies
• Conservation laws for conformally invariant variational problems
• On L(p,q) spaces
• THE ENERGY SPACES OF THE TANGENT POINT ENERGIES
• Repulsive knot energies and pseudodifferential calculus for O’Hara’s knot energy family E ^(α) , α ∈ [2, 3)
• BOUNDEDNESS AND REGULARIZING EFFECTS OF O'HARA'S KNOT ENERGIES
• Classical Fourier Analysis
• Modern Fourier Analysis
• Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems. (AM-105)
• n/p-harmonic maps: Regularity for the sphere case