It is well known that
Grayson's dumbbell neck-pinch<sup>1,2</sup> separates
into disconnected pieces under
mean curvature flow:
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&nbsp;![GraysonDumbells][1]
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<sup>
[Image source: Simplicial Ricci Flow](http://inspirehep.net/record/1249871/plots).
(For contrast, see the earlier MO question,
[Intuition behind the Ricci flow](https://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&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 mean-curvature flow shrinking) been explored?
And perhaps found wanting?

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

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<sup>1</sup>M. A. Grayson, "A short note on the evolution of a surface by its mean curvature," *Duke Math. J.* 58 (3) (1989) 555–558.
([Euclid link](https://projecteuclid.org/euclid.dmj/1077307667).)
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<sup>2</sup>Tobias Holck Colding, William P. Minicozzi II and Erik Kjær Pedersen.
"Mean curvature flow." 
*Bull. Amer. Math. Soc.* 52 (2015), 297-333.
([AMS link](http://www.ams.org/journals/bull/2015-52-02/S0273-0979-2015-01468-0/).)

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