Abstract
We study the all time regularity of the free-boundary problem associated to the deformation of a compact weakly convex surface Σ in ℝ3, with a flat side, by its Gaussian Curvature. We show that under certain necessary regularity and non-degeneracy initial conditions the interface separating the flat from the strictly convex side, remains smooth on 0<t<T c , up to the vanishing time T c of the flat side.
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Daskalopoulos, P., Lee, KA. Worn stones with flat sides all time regularity of the interface. Invent. math. 156, 445–493 (2004). https://doi.org/10.1007/s00222-003-0328-1
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DOI: https://doi.org/10.1007/s00222-003-0328-1