Is there a surgery to lift the corner of the eyes?

Its sounds like what you are looking for is a lateral canthopexy or canthoplasty. This is often done as part of a blepharoplasty. Book a consultation with a local board certified surgeon to have them determine exactly what you need and how much it will cost.

The change you are looking for can be achieve using one of several available techniques. Lateral canthplasty, lateral cathopexy, or lateral retinacular suspension can all achieve this type of lifting effect. Some are less invasive than others and the choice will depend on your overall eye anatomy to some degree. A consultation should be able to determine which is the best choice in your case.

The name of the procedure you are referring to is a lateral canthoplasty.  Seek out a board certified oculoplastic surgeon to discuss your options.  These days we often avoid surgery and are able to achieve more natural appearing results by supporting the corner of the eyelids with filler or tightening the skin with devices such as ThermiRf or Ulthera.  An injection specialist with experience in treating the eyelid area can review all the options with you.Best of luck!

A lateral canthopexy may allow the lateral corner of the eye to be lifted. Best to be seen in person to determine what might be the best approach for you.