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Limit holonomy and extension properties of Sobolev and Yang-Mills bundles

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Abstract

We consider the local behavior of Sobolev connections in a neighborhood of a singularity of codimension 2 and determine sufficient conditions for existence and local constancy of the limit holonomy of such connection. We prove that every Sobolev connection on an mdimensional manifold with locally Lm/2-integrable curvature and trivial limit holonomy extends through singularity of codimension 2. Additionally, if the connection satisfies the Yang-Mills-Higgs equation, the extension also satisfies the equation.

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Authors and Affiliations

  1. Fakultät für Mathematik, Ruhr-Universität Bochum, Universitätsstrasse 150, D-44780, Bochum, Germany

    Vsevolod V. Shevchishin

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  1. Vsevolod V. Shevchishin
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Correspondence to Vsevolod V. Shevchishin.

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Communicated by Alan Huckleberry

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Shevchishin, V.V. Limit holonomy and extension properties of Sobolev and Yang-Mills bundles. J Geom Anal 12, 493–528 (2002). https://doi.org/10.1007/BF02922051

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