TITLE: Avoiding mean-curvature flow dumbbell neck-pinch by inflating a surface
QUESTION [8 upvotes]: It is well known that
Grayson's dumbbell neck-pinch1,2 separates
into disconnected pieces under
mean curvature flow:

 
 
 
 
 

 
 
 
 
 

Image source: Simplicial Ricci Flow.
(For contrast, see the earlier MO question,
Intuition behind the Ricci flow.)


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 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.

1M. 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.)

2Tobias Holck Colding, William P. Minicozzi II and Erik Kjær Pedersen.
"Mean curvature flow." 
Bull. Amer. Math. Soc. 52 (2015), 297-333.
(AMS link.)

REPLY [2 votes]: My question was usefully answered in the comments:
Otis Chodosh pointed me to 
the inverse mean-curvature flow as described, e.g., in this paper:

Huisken, Gerhard, and Tom Ilmanen. "The inverse mean curvature flow and the Riemannian Penrose inequality." Journal of Differential Geometry. 59.3 (2001): 353-437.

and Willie Wong explained how it would evolve dumbbells.
Rbega pointed me to this paper

Kazhdan, Michael, Jake Solomon, and Mirela Ben‐Chen. "Can Mean‐Curvature Flow be Modified to be Non‐singular?." Computer Graphics Forum. Vol. 31. No. 5. Blackwell Publishing Ltd, 2012.

which contains this image of their modified "conformalized mean-curvature flow" applied
to dumbbells: