Obstructions to the existence of solutions of the self-dual Einstein-Maxwell-Higgs equations on a compact surface
Abstract
In this note we present an obstruction to the existence of solutions to the self-dual Einstein-Maxwell-Higgs equations on a compact surface, which depends on the multiplicities of the zeroes of the Higgs field and the vortex number N. In particular, we exhibit infinitely many examples of Higgs fields for which solutions cannot exist.
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