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The Type II seesaw model requires that its scalar doublet $H$ and triplet$\Delta$ get specific patterns of VEVs $\langle H\rangle\propto(0,1)^{T}$ and$\langle\Delta\rangle\propto(0,0,1)^{T}$ to accommodate neutrino masses.However, other types of minima could also exist in the scalar potential, whichmay strongly contradict to experimental observations. This paper studies whenthe minimum at $\langle H\rangle\propto(0,1)^{T}$ and$\langle\Delta\rangle\propto(0,0,1)^{T}$ will be global and finds the necessaryand sufficient condition for that, assuming that the lepton number violatingterm $H^{2}\Delta$ in the potential is perturbatively small.

Minima of the Scalar Potential in the Type II Seesaw Model: From Local to Global