Topological and analytical properties of Sobolev bundles, I: The critical case
Topological and analytical properties of Sobolev bundles, I: The critical case
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DOI：
10.1007/s10455-008-9137-5
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发表时间：
2009-05
影响因子：
0.7
通讯作者：
T. Isobe
中科院分区：
文献类型：
--
作者：
T. Isobe
我们研究了索博列夫丛的拓扑性质和解析性质之间的相互关系，并描述了它们在主丛变分问题上的一些应用。我们特别证明了 M 上定义的类 W2,m/2 的 Sobolev 主 G 丛的范畴等价于 M 上的平滑主 G 丛的范畴，并给出了具有指定同构类的平滑主 G 丛的弱顺序闭包的表征。我们还证明了最小化共形不变杨-米尔斯泛函序列的拓扑紧性结果。
We study the interrelationship between topological and analytical properties of Sobolev bundles and describe some of their applications to variational problems on principal bundles. We in particular show that the category of Sobolev principalG-bundles of classW2,m/2defined overMmis equivalent to the category of smooth principalG-bundles onMand give a characterization of the weak sequential closure of smooth principalG-bundles with prescribed isomorphism class. We also prove a topological compactness result for minimizing sequences of a conformally invariant Yang-Mills functional.