The DNA Inequality in Non-Convex Regions
نویسنده
چکیده
The DNA Inequality states that the average curvature of a curve inside of a given closed figure exceeds the average curvature of the figure. In the paper by Lagarias and Richardson (1997) that proved it for convex figures, the question arose if it could be possible to prove it for some non-convex region; the authors suggested L-Shaped regions. In this paper, we disprove the conjecture for L-Shapes and show that the DNA inequality holds for (another) non-convex region, in fact for a quadrilateral.
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