Good point. An infinitely quick circle would reduce to a point. Morphing a 2D map in 3D, I would imagine the inside of the circle like a balloon with the circl

Good point. An infinitely quick circle would reduce to a point. Morphing a 2D map in 3D, I would imagine the inside of the circle like a balloon with the circle as the opening. Reducing that to 2D seems impossible without breaking it somehow. I guess the problem is worth at least a paper, if not a dissertation. Maybe there is some esoteric math paper in topology which already solved that? Or has proven it impossible?