R. Hamilton in [Ham1] proved that a planar region on a convex hypersurface does not "instantly bend", and so instantly vanish, under Gauss curvature flow. We demonstrate that if the surface is smooth, the planar region in fact does not move at all for some positive time. This is a sort of geometric analogue of "waiting time" phenomena for the porous medium equation.
|Number of pages||24|
|Journal||Indiana University Mathematics Journal|
|Publication status||Published - 1999 Mar|
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