It is well known that
Grayson's dumbbell neck-pinch separates
into disconnected pieces under
Ricci flow:
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&nbsp;![GraysonDumbells][1]
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<sup>
[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).)
</sup>
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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&mdash;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"&mdash;zero surface-to-surface friction&mdash;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.

  [1]: https://i.sstatic.net/b3Yts.jpg