通过双覆盖和相对于平面集的最小连接将Sobolev映射提升到闭合黎曼流形
Liftings of Sobolev maps into closed Riemannian manifolds via double coverings and minimal connections relative to planar sets, with an application to ferronematics
AI总结：
本文通过双覆盖和最小连接方法研究Sobolev映射的提升，并应用于铁磁流体模型的最小化问题。
AI中文摘要：
我们考虑从平面域到闭合黎曼流形的Sobolev映射及其通过目标的双覆盖的BV提升。我们建立了提升的跳跃长度的精确下界，以一种几何量表示：相对于域的非定向奇点的最小连接。作为应用，我们分析了在``混合''边界条件下二维铁磁流体模型的最小化问题--即，对于液晶序参量采用Dirichlet条件，对于磁化矢量采用Neumann条件。
英文摘要：
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.
