S. Segura Gomis

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Let K ⊂ R 2 be a compact convex set in the plane. A halving chord of K is a line segment pˆp, p, ˆ p ∈ ∂K, which divides the area of K into two equal parts. For every direction v there exists exactly one halving chord. Its length h A (v) is the corresponding (area) halving distance. In this article we give inequalities relating the minimum and maximum(More)
Let E be a subset of a convex, open, bounded, planar set G. Let P (E, G) be the relative perimeter of E (the length of the boundary of E contained in G). We obtain relative geometric inequalities comparing the relative perimeter of E with the relative diameter of E and with its relative inradius. We prove the existence of both extremal sets and maximizers(More)
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