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Isobe, Takeshi

Topological and analytical properties of Sobolev bundles. II. Higher dimensional cases. (English) Zbl 1250.58004

Rev. Mat. Iberoam. 26, No. 3, 729-798 (2010).
Summary: We define various classes of Sobolev bundles and connections and study their topological and analytical properties. We show that certain kinds of topologies (which depend on the classes) are well-defined for such bundles and they are stable with respect to the natural Sobolev topologies. We also extend the classical Chern-Weil theory for such classes of bundles and connections. Applications related to variational problems for the Yang-Mills functional are also given.
For Part I see [Ann. Global Anal. Geom. 35, No. 3, 277–337 (2009; Zbl 1166.58003)].

Cited in 6 Documents

MSC:

58B20 Riemannian, Finsler and other geometric structures on infinite-dimensional manifolds
58D15 Manifolds of mappings
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
57R22 Topology of vector bundles and fiber bundles
58E15 Variational problems concerning extremal problems in several variables; Yang-Mills functionals

Keywords:

Sobolev bundle; topology of bundle; Yang-Mills functional; variational problem

Citations:

Zbl 1166.58003
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Full Text: DOI Euclid

References:

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