How to fix hollow under eyes? (Photos)

At least from the photos provided, there appears to be considerable volume deficit in the cheeks, leading to their flattening, and (since the upper cheeks are the primary support for the under-eyes) the under-eye hollows that disturb you. Accordingly, the skillful use of an appropriately robust HA volumizing filler for the cheeks will not only restore a more normal contour to that area, but will secondarily soften the smile folds and address the under-eye hollows and create a smoother, more natural transition between the upper cheeks and the under-eyes.
In experienced hands, this nonsurgical treatment should take no more than about fifteen minutes to perform with immediate results and little to no significant downtime.
You would be wise to consult with an experienced, board certified cosmetic dermatologist filler expert.
Hope this helps and best of luck.