At least from the photos provided, the kind of under eye hollowing shown can often be easily and quickly treated with fillers. In general, a supportive volumizing filler, such as Voluma XC, can be used to restore or in some cases to create a sufficient supportive foundation for the under eye region, which alone typically makes a secondary improvement in the appearance of hollowed under eyes. The use of less robust, filler, if still needed, such as Belotero Balance or Teosyal Redensity II, may be used to create a smooth transition between the upper cheek and lower lid regions. Fat injections, despite the allure, have a number of drawbacks, which is why I gave up using this approach many years ago. For one thing, fat severed from its original blood supply, seldom lasts more than traditional fillers in the transpanted locations. What's more fat transfer is a relatively expensive two-step minimally invasive process that engenders some real downtime. (removing the fat with large cannulas from the belly, buttocks or thighs and reinjecting it with large cannulas into the new location). Moreover, the fat from say the belly retains, wherever it is relocated to, the belly fat's propensity to put on a "midriff bulge" with age, which can be quite displeasing and difficult to deal with it later on. Surgery, with all its expense and downtime, is of course does remain an option. But it would seem reasonable to explore a noninvasive approach first that typically results in an immediate "Wow!" reaction and has a surprisingly protracted durability of response. Be sure of course to consult with a board certified aesthetic physician injector and make sure to ask to see his/her personal befores and afters before agreeing to proceed. Best of luck.
