I'm not used to having what ski instructors tell me show up at the World Championship level, but that is exactly what's happening now.
A basic truism of skiing is keep your weight on the outside ski - there are a ton of references on this, but my fav is Lito Tejada-Flores with his DVDs and web site: Breakthrough on skis. It's easy to think that this is just something they tell you to help you learn, but I'm watching the Alpine World Cup on Universal Sports Womens Super G that was just held 3 days ago on Feb 3rd (well the whole competition will be going on for a while) in Val d'isere, France. This is a tough, very curvy Super-G course and the object lessons were (a) memorize the course carefully (you don't get to practice on it) as there were a lot of missed gates and (b) keep your weight on the outside ski. You are going at very unforgiving speeds: if you lean in you will go down or your inside ski could catch an edge and send you flying. While there were good examples of that in that competition, an excellent example of that happening, also happened on Dec 5th at Lake Louise, NY to Romanian Edith Miklos here. A different less dramatic example is here.
American Lyndsey Vonn is currently in the lead of the entire competition (she did win the Super G event with a beautiful run, and also Lake Louise as well), and will no doubt become a household name during the Olympics in Vancouver. The results page is here.
So keep that weight on the outside ski when turning.