Abstract

We study the second derivative Q_cλ of the Yang–Mills–Higgs functional with structure group SU(2) at a spherically symmetric critical point c_λ when the self-interaction parameter λ is not close to 0. We find that if Q_cλ0 is non-negative and with kernel consisting entirely of translation modes then positivity persists in a neighborhood of λ₀. In particular, we show that if translation modes always account for the whole kernel then Q_cλ is always non-negative. This extends our previous results for λ in an neighborhood of 0.

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