02/11/2013 at 08:00 AM EST
Lindsey Vonn is recuperating after surgery on Sunday to repair a torn stabilizing ligaments in her knee and a fractured shin. Her doctor said he is hopeful for a full recovery.
Vonn, 28, injured herself
on Feb. 5 while competing at the FIS Alpine Ski World Championships in Schladming, Austria, where she was air-lifted from the slopes.
The surgery took place at the Vail Valley Surgery Center and was conducted by Dr. Bill Sterett of Vail-Summit Orthopaedics, who is the head physician for the U.S. Women's Alpine Ski Team.
Sterett said in a statement that Vonn was resting comfortably after the surgery to repair a torn ACL/MCL (anterior cruciate ligament/medial collateral ligament) and lateral tibial plateau fracture.
"The overall success rate for ACL/MCL surgery is very good," Sterett said. "Modern surgical techniques combined with aggressive rehabilitation will help Lindsey make a full recovery."
He added: "She will do everything in her power to return as quickly as possible to competitive skiing."
Vonn has been linked romantically
with Tiger Woods
. After her accident in Austria, she flew home to the United States on his private jet as a source close to PEOPLE said the star athletes were spending more time together
Sterett said that knee injuries are not uncommon for competitive skiers. He noted that Picabo Street returned to competition after reconstructive surgery to win a gold medal at the 1998 Olympic Games held in Nagano, Japan.
The competitive Vonn vowed after her accident to return to competitive skiing
in November and to be ready for next year's Winter Olympics in Sochi, Russia.