Codimension one minimal cycles with coefficients inZ orZ p , and variational functionals on fibered spaces |
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Authors: | Sisto Baldo Giandomenico Orlandi |
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Affiliation: | (1) Dipartimento di Matematica, Universitá della Basilicata (Potenza), Italia;(2) Dipartimento di Matematica, Universitá di Verona, Italia |
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Abstract: | Given a compact, oriented Riemannian manifold M, without boundary, and a codimension-one homology class in H* (M, Z) (or, respectively, in H* (M, Zp) with p an odd prime), we consider the problem of finding a cycle of least area in the given class: this is known as the homological Plateau’s problem. We propose an elliptic regularization of this problem, by constructing suitable fiber bundles ξ (resp. ζ) on M, and one-parameter families of functionals defined on the regular sections of ξ, (resp. ζ), depending on a small parameter ε. As ε → 0, the minimizers of these functionals are shown to converge to some limiting section, whose discontinuity set is exactly the minimal cycle desired. |
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Keywords: | KeywordHeading" >Math Subject Classifications 42Q20 49Q05 |
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