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Publication 109

A Sharp Lower Bound On The Polygonal Isoperimetric Deficit


CMUE. Indrei
Center for Nonlinear Analysis
Carnegie Mellon University
Pittsburgh PA 15213-3890 USA

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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