At the beginning of his sports career, Korotkow was an alpine ski racer , but was not very successful. His best result in an FIS race is third place in December 2008. In the same month he contested his last ever alpine race. His first participation in an international ski cross race was in March 2006 on the occasion of the Freestyle Junior World Championships in Krasnoye Ozero, where he finished fifth.
Korotkow made his debut in the World Cup on January 12th, 2008 in Les Contamines , where he finished 15th and won World Cup points. The best result in his first season was an 11th place a week later in Kreischberg . In the following World Cup season 2008/09 he did not get beyond a 23rd place, but won the Russian championship title for the first time. In January 2010 Korotkow made it into the top ten in the World Cup for the first time, and at the 2010 Winter Olympics he came in 25th. On January 16, 2011, he achieved his first World Cup podium finish with third place in Les Contamines. At the start of the 2010/11 season, Korotkow came second twice in Innichen , which is equivalent to his best results in the World Cup so far.