S. Segura Gomis

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Let K ⊂ R be a compact convex set in the plane. A halving chord of K is a line segment pp̂, p, p̂ ∈ ∂K, which divides the area of K into two equal parts. For every direction v there exists exactly one halving chord. Its length hA(v) is the corresponding (area) halving distance. In this article we give inequalities relating the minimum and maximum (area)(More)
In this paper we summarize the known results and the main tools concerning complete systems of inequalities for families of convex sets. We discuss also the possibility of using these systems to determine particular subfamilies of planar convex sets with specific geometric significance. We also analyze complete systems of inequalities for 3-rotationally(More)
OBJECTIVES To evaluate the therapeutic and diagnostic potential of large loop excision of the transformation zone (LLETZ) in the management of cervical dysplasia (CD) when colposcopy is satisfactory; to determine if there is a relationship between completeness of excision and outcome. STUDY DESIGN Ninety loop diathermies performed in the management of CD(More)
If K is a convex body in the Euclidean space E, we consider the six classic geometric functionals associated with K: its n-dimensional volume V , (n− 1)-dimensional surface area F , diameter d, minimal width ω, circumradius R and inradius r. We prove that the n-spherical symmetric slices are the convex bodies that maximize both, the volume and the surface(More)
In this work we study the fencing problem consisting of finding a trisection of a 3-rotationally symmetric planar convex body which minimizes the maximum relative diameter. We prove that an optimal solution is given by the so-called standard trisection. We also determine the optimal set giving the minimum value for this functional and study the(More)
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