Fat transfer or Voluma - which procedure would be best for lifting the face and correcting gaunt, hollow cheeks?

You did not post photos, so I cannot be specific. For overall improvement in volume, Sculptra works well. I was first approved to treat the hollow faces of patients with HIV.

Both fat transfer and Voluma can be used to add volume to the face. Fat transfer has more longevity but is more involved. Another option is Renuva which gives the immediate result of filler with the benefit of the product being replaced naturally by your own fat over time. Yet another option to conisder is Sculptra which works differently than fillers. I've included a video on Sculptra that I hope you find helpful. I encourage you to meet with an expert injector to determine the best recommendation for you.

Fat transfer, Voluma and other dermal fillers can all be used to add volume to the face. When volume is added to the face, it can create some lifting, but generally not as much lifting as surgery can create.