It is well known that Grayson's dumbbell neck-pinch separates into disconnected pieces under Ricci flow:

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         ![GraysonDumbells][1]
          ^{[Image source: Simplicial Ricci Flow](http://inspirehep.net/record/1249871/plots). (See also the earlier MO question, [Intuition behind the Ricci flow](http://mathoverflow.net/a/143146/6094).)}

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Intuitively, it seems there might be another route to morph any genus-zero surface embedded in $\mathbb{R}^3$ to a round sphere, via "inflation." Imagine slowly pumping air into the surface, attempting to inflate it to a sphere. Treat the surface as elastic/stretchable, but do not allow the surface to pass through itself—it should remain embedded. This would certainly work for the dumbbell, but might get stuck for a pretzel-twisted surface. I wonder if rendering the surface "slippery"—zero surface-to-surface friction—would prevent it from getting stuck.

Q. Has some notion of inflating a surface (analogous to Ricci-flow shrinking) been explored? And perhaps found wanting?

I realize this question is not formalized, but I suspect the Ricci-flow experts can answer despite its vagueness.