Geodesic Incompleteness in the ℂP1 Model on a Compact Riemann Surface

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It is proved that the moduli space of static solutions of the ℂP1 model on spacetime σ × ℝ, where σ is any compact Riemann surface, is geodesically incomplete with respect to the metric induced by the kinetic energy functional. The geodesic approximation predicts, therefore, that lumps can collapse and form singularities in finite time in these models.

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