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- W4288595917 abstract "We extend the results of our recent preprint [arXiv: 1811.00515] into higher dimensions $n geq 4$. For minimizing harmonic maps $uin W^{1,2}(Omega,mathbb{S}^2)$ from $n$-dimensional domains into the two dimensional sphere we prove: (1) An extension of Almgren and Lieb's linear law, namely [mathcal{H}^{n-3}(textrm{sing} u) le C int_{partial Omega} |nabla_T u|^{n-1} ,dmathcal{H}^{n-1};] (2) An extension of Hardt and Lin's stability theorem, namely that the size of singular set is stable under small perturbations in $W^{1,n-1}$ norm of the boundary." @default.
- W4288595917 created "2022-07-29" @default.
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- W4288595917 date "2019-02-08" @default.
- W4288595917 modified "2023-09-27" @default.
- W4288595917 title "On the size of the singular set of minimizing harmonic maps into the 2-sphere in dimension four and higher" @default.
- W4288595917 doi "https://doi.org/10.48550/arxiv.1902.03161" @default.
- W4288595917 hasPublicationYear "2019" @default.
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