[ehartsuyker]

Actually, not. The definition of convex is that given a point A and a point B and a line between A and B, all points on the line AB are in the interior space of the solid.

Inflating two adjacent surfaces creates a valley along the pre-existing edge between the two of them and fails the above definition.

[JoeAltmaier]

Yet that's what the OP describe. Remember, the edge was a "mountain" to begin with, you have some wiggle room. That's the observation that the whole paper is based upon.