They're known as great knives. You'll like it.
As for asymmetrical double bevel knives: think of the flat side as the part that allows you to get the centre of the bevel closer to the main piece of food you're cutting (which, theoretically allows thinner slices, more easily). The convexing naturally thickens a blade, but is a bit of a necessary evil. By convexing on one side, the food release is increased, but the thinness is not as badly effected as it is on a knife with both faces having convexing. Convexing is great TO AN EXTENT, but the difference between a great convex and a bad one is less than a hair width, and also depends on the location of the "radius".
With all of the being said, a single bevel knife with a flat grind release food beautifully, because the transition at the shinogi line pushes the food away. However, a yanagiba would wedge like all hell in a potato, or other hard food items, unless you were attacking it from the side, with thin slices and never splitting it down the middle.