Fermi surface in alkaline earth metals- metallic behaviour in different dimensions

arpitloveslyf

In the fermi surface diagrams of the alkaline earth metals, in order to check the metallic behaviour, following equations are given

highest energy of the lower band = energy of free electron at (∏/a, 0) + Eg (center)/2
,lowest energy of the upper band = energy of free electron at (∏/a, ∏/a) - Eg (corner)/2

Please explain what is Eg (corner ) and Eg( center ) here.
Finally in this question, we have to check that as we increase dimensions, metallic character increases.