A REMARK ON THE JACOBIANS

DOI10.1142/S0219199700000037zbMath1033.49047OpenAlexW1966528074MaRDI QIDQ4513334

Fang-Hua Lin, Feng Bo Hang

Publication date: 14 November 2000

Published in: Communications in Contemporary Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0219199700000037

zbMATH Keywords

Jacobiansvector-valued measuremultiplicity current

Mathematics Subject Classification ID

Variational problems in a geometric measure-theoretic setting (49Q20) Implicit function theorems, Jacobians, transformations with several variables (26B10) Currents in global analysis (58A25)

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\(H^{1/2}\) maps with values into the circle: minimal connections, lifting, and the Ginzburg-Landau equation ⋮ Existence of energy minimizers as stable knotted solitons in the Faddeev model ⋮ The homological singularities of maps in trace spaces between manifolds ⋮ A brief history of the Jacobian ⋮ Functions of bounded higher variation in the fractional Sobolev spaces ⋮ The Jacobian determinant revisited ⋮ On the distributional Jacobian of maps from \(\mathbb{S}^N\) into \(\mathbb{S}^N\) in fractional Sobolev and Hölder spaces ⋮ Estimates for the topological degree and related topics ⋮ \(W^{s,\frac{n}{s}}\)-maps with positive distributional Jacobians ⋮ Coarea formulae and chain rules for the Jacobian determinant in fractional Sobolev spaces ⋮ A variational problem with lack of compactness for \(H^{1/2}(S^{1};S^{1})\) maps of prescribed degree ⋮ Prescribing the Jacobian in critical spaces ⋮ Strong density results in trace spaces of maps between manifolds

Cites Work

• Harmonic maps with defects
• On the singular support of the distributional determinant
• Degree theory of BMO. I: Compact manifolds without boundaries
• Degree theory and BMO. II: Compact manifolds with boundaries. (Appendix with Petru Mironescu)