Faddeev模型分析
Analysis of the Faddeev model
摘要：
本文考虑了Faddeev模型的一个推广，它适用于闭三流形到二球面的映射。给出了光滑$ S^2$值映射的一种新的基于平坦联络的表示.这种表示使我们能够获得一个解析描述的同伦类的$ S^2$值映射，推广到索伯列夫地图。这也导致了一个新的证明一个老定理Pontrjagin。对于推广的Faddeev模型，我们证明了在每个同伦类中极小解的存在性。
英文摘要：
In this paper we consider a generalization of the Faddeev model for the maps from a closed three-manifold into the two-sphere. We give a novel representation of smooth $ S^2$-valued maps based on flat connections. This representation allows us to obtain an analytic description of the homotopy classes of $ S^2$-valued maps that generalizes to Sobolev maps. It also leads to a new proof an old theorem of Pontrjagin. For the generalized Faddeev model, we prove the existence of minimizers in every homotopy class.
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