## How to deform a unit solid cube to a unit ball? [closed]

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?

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.

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 Ricci flow is acting on manifolds without boundary; Please read the FAQ to see which questions are appropriate. – Benoît Kloeckner Jun 16 at 14:01 @Benoît Kloeckner, thanks for your advice. – cookmath Jun 17 at 2:29