The kind of under-eye problem seen in the photos provided is a rather routine cosmetic problem treated practically every day in my cosmetic dermatology practice. Infraorbital tear troughs, dark circles and hollows are in fact some of the most common and troubling problems. Fortunately, there are now many different HA fillers that can be used to treat this. For one thing, there appears here to be quite a bit of cheek volume deficit, and since the upper cheeks constitute a major support for the infraorbital region, the use of a robust HA volumizing filler for the cheeks can give rise to an immediate, on-the-spot improvement not only in the cheeks themselves (to contour a more feminine, heart-shaped, oval face) but in the under-eyes. If still necessary, for further improvement, there are HA fillers designated specifically for under-eye use. From what can be seen in photos, there is little need for any aggressive, invasive, expensive surgery (that runs the risks for infection, scarring and prolonged downtime). You would be wise to consult with an experienced, board certified cosmetic dermatologist filler expert. Treatment typically takes about fifteen minutes to perform and the results typically engender an immediate "Wow!" reaction. Hope this helps and best of luck.