As an outdoors men a myth has been around for longer then I. The myth is , If a bear is running after you just run down a hill, because a bear can not run down a hill and will fall or slow. It is because of the bears body shape. Ever here of a myth like this. It is Canadaian so it has to be true.

I dont' know about grizzlies, but black bears can run down hill. I know because I have seen it often. I live in the mountains of North Carolina, which has plenty of both bears and hills, and they don't seem to have a problem with each other. Again, we only have black bears, but I don't see why other species would have any problem.