An estimate of the Hopf degree of fractional Sobolev mappings

DOI10.1090/proc/15026zbMath1487.55020arXiv1904.12549OpenAlexW3101196863MaRDI QIDQ5111500

Armin Schikorra, Jean Van Schaftingen

Publication date: 27 May 2020

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

Full work available at URL: https://arxiv.org/abs/1904.12549

zbMATH Keywords

Hopf invariantfractional Sobolev spaceGagliardo-Nirenberg inequalitiesHopf degree

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Degree, winding number (55M25) de Rham theory in global analysis (58A12) Homotopy theory (55P99) Hopf invariants (55Q25)

Related Items (4)

Quantitative estimates for fractional Sobolev mappings in rational homotopy groups ⋮ \(W^{s,\frac{n}{s}}\)-maps with positive distributional Jacobians ⋮ Estimates by gap potentials of free homotopy decompositions of critical Sobolev maps ⋮ Hölder-topology of the Heisenberg group

Cites Work

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• Estimates for the topological degree and related topics
• A new estimate for the topological degree
• The Jacobian determinant revisited
• Connecting rational homotopy type singularities
• Factorization theorems for Hardy spaces in several variables
• Minimizing fibrations and \(p\)-harmonic maps in homotopy classes from \(S^3\) into \(S^2\)
• Über die Abbildungen der dreidimensionalen Sphäre auf die Kugelfläche
• Gagliardo-Nirenberg inequalities and non-inequalities: the full story
• Sharp commutator estimates via harmonic extensions
• Coarea formulae and chain rules for the Jacobian determinant in fractional Sobolev spaces
• Estimates by gap potentials of free homotopy decompositions of critical Sobolev maps
• Some results on maps that factor through a tree
• Homotopy groups of spheres and Lipschitz homotopy groups of Heisenberg groups
• Optimal constant in a new estimate for the degree
• An existence theorem for surfaces of constant mean curvature
• Multiple solutions ofH-systems and Rellich's conjecture
• The Characterisation of the Regularity of the Jacobian Determinant in the Framework of Potential Spaces
• Lifting, degree, and distributional Jacobian revisited
• Classical Fourier Analysis
• Modern Fourier Analysis
• An Expression of Hopf's Invariant as an Integral
• Metric structures for Riemannian and non-Riemannian spaces. Transl. from the French by Sean Michael Bates. With appendices by M. Katz, P. Pansu, and S. Semmes. Edited by J. LaFontaine and P. Pansu
• Compactness for maps minimizing the \(n\)-energy under a free boundary constraint

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