The term "under-eye hollows" is best avoided. Why? "Under" is too imprecise and can be used to indicate anything from eyelid hollowness to cheek bone depression to midface descent to dark circles, all of which are different conditions requiring different treatments.
Essentially, the lower eyelid begins at the eyelashes and ends just above the rim of bone beneath the eye. Below that bony rim sits the top of the cheek. The anatomy of these two structures is distinct.
Imprecise terminology is confusing and can, unfortunately, result in incorrect treatment. The terms below are preferable . . .