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On a problem of Seiberg and Witten

David E. Barrett — 1998

Annales Polonici Mathematici

We describe alternate methods of solution for a model arising in the work of Seiberg and Witten on N = 2 supersymmetric Yang-Mills theory and provide a complete argument for the characterization put forth by Argyres, Faraggi, and Shapere of the curve I m a D / a = 0 .

Failure of averaging on multiply connected domains

David E. Barrett — 1990

Annales de l'institut Fourier

We show that for every open Riemann surface X with non-abelian fundamental group there is a multiple-valued function f on X such that the fiberwise convex hull of the graph of f fails to contain the graph of a single-valued holomorphic function on X .

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