Hi Danaverno,
Under eye hollows are most commonly caused by lifestyle issues such as dehydration, lack of sleep, stress, imbalanced diet, so on. However, in some cases it can also be due to genetics, sun exposure, allergies, etc.
In the former case, lifestyle modification such as good sleep, hydration, a balanced diet does wonders to the skin and therefore the under-eye hollows.
In the latter case, such as genetics or sun exposed skin, provided you do not have any other conditions which need to be treated, hyaluronic acid fillers does wonders and masks the shadows cast by the hollows.
The decision to treat using fillers is taken only after a visit to your plastic surgeon.
Hope this answer helps.
Cheers,
Dr. Harish Kumar Kabilan
Kalp aesthetics