The women's competition is heading for a thrilling finale in Thursday's free dance as only a fine margin separates leader Kim from Russian Adelina Sotnikova and 2012 world champion Carolina Kostner of Italy who is third.
There are finals in women's ice hockey and curling, with Canada featuring in both.
The ice hockey final pits the United States against Canada, far and away the strongest tams in the sport.
Canada have had the upper hand recently. They beat the Americans 2-0 in the final at the 2010 Vancouver Games and also defeated their biggest rival 3-2 in the preliminary round in Sochi.
In curling, Canada's women face Sweden in another repeat of the 2010 final. The Swedes are seeking a third successive gold but face a tough challenge against a Canadian team who have marched to the final without suffering defeat.
Two medals are up for grabs in freestlye skiing at the Extreme Park.
France's Jean-Frederic Chapuis is the current world champion in men's ski cross and Swiss Alex Fiva has been in fine form in the World Cup but few events at the Sochi Olympics are as hard to predict.
American X-Games champion Maddie Bowman and Canadian runner-up Rosalind Groenewoud will start as favourites as women's ski halfpipe makes its Olympic debut.
Germany, backed by gold medalist Eric Frenzel, looks to be far too strong for opponents in Nordic Combined team event.