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This paper deals with a curve evolution problem which, if the curvature of the initial convex curve satisfies a certain pinching condition, keeps the convexity and preserves the perimeter, while increasing the enclosed area of the evolving curve, and which leads to a limiting curve of constant width. In particular, under this flow the limiting curve is a circle if and only if the initial convex curve is centrosymmetric.

Evolving convex curves to constant-width ones by a perimeter-preserving flow