Liftings of Sobolev maps into closed Riemannian manifolds via double coverings and minimal connections relative to planar sets, with an application to ferronematics
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866914363372208128 |
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| author | Canevari, Giacomo Dipasquale, Federico Luigi Stroffolini, Bianca |
| author_facet | Canevari, Giacomo Dipasquale, Federico Luigi Stroffolini, Bianca |
| contents | We consider Sobolev maps from a planar domain into a closed Riemannian manifold and their BV liftings via a double covering of the target. We establish a sharp lower bound on the jump length of the lifting, expressed in terms of a geometric quantity: the minimal connection, relative to the domain, of the non-orientable singularities. As an application, we analyse minimisers of a two-dimensional model of ferronematics under ``mixed'' boundary conditions -- that is, Dirichlet conditions for the liquid crystal order parameter and Neumann conditions for the magnetisation vector. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_01985 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Liftings of Sobolev maps into closed Riemannian manifolds via double coverings and minimal connections relative to planar sets, with an application to ferronematics Canevari, Giacomo Dipasquale, Federico Luigi Stroffolini, Bianca Analysis of PDEs Functional Analysis 35Q56, 76A15, 49Q15, 26B30 We consider Sobolev maps from a planar domain into a closed Riemannian manifold and their BV liftings via a double covering of the target. We establish a sharp lower bound on the jump length of the lifting, expressed in terms of a geometric quantity: the minimal connection, relative to the domain, of the non-orientable singularities. As an application, we analyse minimisers of a two-dimensional model of ferronematics under ``mixed'' boundary conditions -- that is, Dirichlet conditions for the liquid crystal order parameter and Neumann conditions for the magnetisation vector. |
| title | Liftings of Sobolev maps into closed Riemannian manifolds via double coverings and minimal connections relative to planar sets, with an application to ferronematics |
| topic | Analysis of PDEs Functional Analysis 35Q56, 76A15, 49Q15, 26B30 |
| url | https://arxiv.org/abs/2603.01985 |