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A topological lower bound on the Skyrme energy which depends explicity on thepion mass is derived. This bound coincides with the previously best known boundwhen the pion mass vanishes, and improves on it whenever the pion mass isnon-zero. The new bound can in particular circumstances be saturated. Newenergy bounds are also derived for the Skyrme model on a compact manifold, forthe Faddeev-Skyrme model with a potential term, and for theAratyn-Ferreira-Zimerman and Nicole models.

Topological energy bounds for the Skyrme and Faddeev models with massive pions