Minima of the Scalar Potential in the Type II Seesaw Model: From Local   to Global
  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, which may strongly contradict to experimental observations. This paper studies when the minimum at $\langle H\rangle\propto(0,1)^{T}$ and $\langle\Delta\rangle\propto(0,0,1)^{T}$ will be global and finds the necessary and sufficient condition for that, assuming that the lepton number violating term $H^{2}\Delta$ in the potential is perturbatively small. 
Xun-Jie Xu
hep-ph