The effect of the ricci flow on the 2D manifold is really amazing.
But how about the ricci flow on a 3D manifold? Could the ricci flow deform a 3D unit solid cube to a 3D unit ball?
Link: 3D cube to 3D unit ball
Maybe it could not beacause the 3D unit ball is not ricci flat. Am I right? If the ricci flow couldn't do it, is there any geometric flow that can do such a transformation?
And I have a further question. If there is a small cubic hole in a large cubic, which mathematical tool can I use to deform it into a structure with a small spherical hole in a large ball?
PS. Maybe I didn't tag this question well. As a freshman, I find the formulas of ricci flow are somewhat too abstract to understand. But I am trying hard to grasp the ideas.