Analysis of S2-Valued Maps and Faddeev’s Model
Analysis of S2-Valued Maps and Faddeev’s Model
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S2 值图和 Faddeev 模型的分析
DOI：
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发表时间：
2005
期刊：
影响因子：
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通讯作者：
L. Kapitanski
中科院分区：
文献类型：
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作者：
D. Auckly;L. Kapitanski
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S2-值映射基于平坦联络的一种新表示。这种表示使我们能够获得一个解析描述的同伦类的S2值映射，推广到索伯列夫映射。这也导致了一个新的证明的老定理Pontrjagin。对于广义Faddeev模型，我们证明了每个同伦类中最小值的存在性。
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 S2-valued maps based on flat connections. This representation allows us to obtain an analytic description of the homotopy classes of S2-valued maps that generalizes to Sobolev maps. It also leads to a new proof of an old theorem of Pontrjagin. For the generalized Faddeev model, we prove the existence of minimizers in every homotopy class.