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If you have a piece of paper that is furled and unfurled so that it's in the shape of part of a parabola, and knowing that if you leave it, it'll flatten itself after time, would it flatten faster if you leave it as a right-way-up parabola, or an upside-down parabola? More particularly, I was wondering what factors would influence the flattening rate.

Note: It would be $y = kx^2$ and $y = -kx^2 + l$ on a 3-D graph, but extended perpendicularly into the $z$-axis

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Well, I can list out the forces which come to my mind as of now, 1. Atmospheric Air pressure 2. gravity force of the paper itself. –  Vineet Menon Oct 30 '11 at 15:48
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