The Non-collapsing Property on Planar Convex Curves Deformed by Power Function of Curvature
In this paper,we consider the non-collapsing property on a class of planar convex curves deformed by non-linear curvature flow.Firstly,we give the definition of the inner non-collapsing property and the outer non-collapsing property on planar curves,then by defining a function Z,we prove that the inner non-collapsing property on planar curves is equivalent to the non-negativity of Z and the outer non-collapsing property on planar curves is equivalent to the non-positivity of Z.Finally,we use maximum principle to prove the non-collapsing property on the planar convex curve shortening flow is maintained under some conditions.
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