Geodesic
Conditions for certain Higgs potentials to be bounded below
Teoretičeskaâ i matematičeskaâ fizika, Tome 62 (1985) no. 1, pp. 87-96

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Necessary and sufficient conditions are obtained for Higgs potentials to be bounded below when they are constructed from: 1) two doublets, and also two doublets and a singlet of $SU(2)$, 2) the adjoint and vector representations of $SO(n)$. For a potential constructed from the adjoint and fundamental multiplets of $SU(n)$, the problem of necessary and sufficient conditions has been only partly solved. 
@article{TMF_1985_62_1_a5,
     author = {K. G. Klimenko},
     title = {Conditions for certain {Higgs} potentials to be bounded below},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {87--96},
     publisher = {mathdoc},
     volume = {62},
     number = {1},
     year = {1985},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1985_62_1_a5/}
}
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K. G. Klimenko. Conditions for certain Higgs potentials to be bounded below. Teoretičeskaâ i matematičeskaâ fizika, Tome 62 (1985) no. 1, pp. 87-96. http://geodesic.mathdoc.fr/item/TMF_1985_62_1_a5/