On convexity of simple closed frontals

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Abstract

We study convexity of simple closed frontals in the Euclidean plane by using the curvature of Legendre curves. We show that for a Legendre curve, the simple closed frontal is convex if and only if the sign of both functions of the curvature of the Legendre curve does not change. We also give some examples of convex simple closed frontals.

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