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Weak Closure of Singular Abelian L p-Bundles in 3 Dimensions

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Abstract

We prove the closure for the sequential weak L p-topology of the class of vector fields on B 3 having integer flux through almost every sphere. We show how this problem is connected to the study of the minimization problem for the Yang–Mills functional in dimension higher than critical, in the abelian case.

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Authors and Affiliations

  1. Departement Mathematik, HG F 28.1, Rämistrasse 101, 8092, Zürich, Switzerland

    Mircea Petrache & Tristan Rivière

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  1. Mircea Petrache
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  2. Tristan Rivière
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Correspondence to Tristan Rivière.

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Petrache, M., Rivière, T. Weak Closure of Singular Abelian L p-Bundles in 3 Dimensions. Geom. Funct. Anal. 21, 1419–1442 (2011). https://doi.org/10.1007/s00039-011-0139-2

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  • DOI: https://doi.org/10.1007/s00039-011-0139-2

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