For any convex n-gon P we consider the polygons obtained by dropping a vertex or an edge of P. The area distance of P to such (n - 1)-gons, divided by the area of P, is an affinely invariant functional on n-gons whose maximizers coincide with the affinely regular polygons. We provide a complete proof of this result. We extend these area functionals to planar convex bodies and we present connections with the affine isoperimetric inequality and parallel X-ray tomography
AFFINELY REGULAR POLYGONS AS EXTREMALS OF AREA FUNCTIONAL
M LONGINETTI;
2008
Abstract
For any convex n-gon P we consider the polygons obtained by dropping a vertex or an edge of P. The area distance of P to such (n - 1)-gons, divided by the area of P, is an affinely invariant functional on n-gons whose maximizers coincide with the affinely regular polygons. We provide a complete proof of this result. We extend these area functionals to planar convex bodies and we present connections with the affine isoperimetric inequality and parallel X-ray tomographyFile in questo prodotto:
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