A sharp lower bound on the polygonal isoperimetric deficit

Indrei, Emanuel

doi:10.1090/proc/12947

A sharp lower bound on the polygonal isoperimetric deficit
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by Emanuel Indrei PDF

Proc. Amer. Math. Soc. 144 (2016), 3115-3122 Request permission

Abstract:

It is shown that the isoperimetric deficit of a convex polygon $P$ admits a lower bound in terms of the variance of the radii of $P$, the area of $P$, and the variance of the barycentric angles of $P$. The proof involves circulant matrix theory and a Taylor expansion of the deficit on a compact manifold.

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