The area under the eye is full of pitfalls for any kind of therapy.
First of all, there are two types of skin next to each other. There is eyelid skin which is thin and adherent to the muscle underneath, and there is cheek skin which is thicker and has fat underneath it.
Secondly, the eyelid skin has usually "slid" over the rim of the cheek bone, as the cheek fat and skin slide down with ageing. The boundary between the eyelid skin and cheek skin is called the "tear trough". This is usually the hollow that people object to because the thin eyelid skin transitions into a thick layer of fat covered with thicker skin, so it looks like a hollow.
It is tempting to try to "fill" the hollow by injecting under it, but that risks creating visible lumps of fat under the thin eyelid skin.
I find it more reliable to inject and expand the cheek skin close to the nose to raise the tear trough and move the eyelid skin up.
You can read a little bit more at the link below.
