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arXiv · 2603.01985

Liftings of Sobolev maps into closed Riemannian manifolds via double coverings and minimal connections relative to planar sets, with an application to ferronematics

Giacomo Canevari·Federico Luigi Dipasquale·Bianca Stroffolini
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Abstract

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.

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Giacomo Canevari, Federico Luigi Dipasquale, Bianca Stroffolini. 2026-03-02. Liftings of Sobolev maps into closed Riemannian manifolds via double coverings and minimal connections relative to planar sets, with an application to ferronematics. https://arxiv.org/abs/2603.01985

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