If the area under the eyes is hollow, hyaluronic acid filler like Restylane can be used to fill it. Surgery can tighten the skin but without restoring volume to the area, it will still look hollow.
Under eye hollows or circles form from loss of volume in soft tissues (primarily collagen and elastin in the skin), fat and bone of the area surrounding the eye.
In order to rejuvenate the eye area, volume needs to be restored.
Injections of hyaluronic acid fillers in the periorbital area must be done with great care and expertise. The choice of filler is important in how much lift and how much swelling there will be after the procedure.
The eyelid area is also highly vascular so bruising can result from injections. Make sure you are not taking any over the counter or non-prescribed blood thinning medications for 2 weeks prior to the procedure. Those include aspirin, NSAIDs like ibuprofen or naproxen, gingko biloba, fish oil, vitamin E and multivitamins containing these. If you are taking a prescribed blood thinner, do not discontinue that, but make your doctor aware that you are taking it.
Consult a board-certified dermatologist or plastic surgeon with training and experience in tear trough injections.