Open Access
Decembar, 2007 Optimizing geometric measures for fixed minimal annulus and inradius
María A. Hernández Cifre, Pedro J. Herrero Piñeyro
Rev. Mat. Iberoamericana 23(3): 953-971 (Decembar, 2007).


In this paper we relate the minimal annulus of a planar convex body $K$ with its inradius, obtaining all the upper and lower bounds, in terms of these quantities, for the classic geometric measures associated with the set: area, perimeter, diameter, minimal width and circumradius. We prove the optimal inequalities for each one of those problems, determining also its corresponding extremal sets.


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María A. Hernández Cifre. Pedro J. Herrero Piñeyro. "Optimizing geometric measures for fixed minimal annulus and inradius." Rev. Mat. Iberoamericana 23 (3) 953 - 971, Decembar, 2007.


Published: Decembar, 2007
First available in Project Euclid: 27 February 2008

zbMATH: 1149.52009
MathSciNet: MR2414499

Primary: 52A10 , 52A38 , 52A40

Keywords: area , circumradius , Convex bodies , diameter , inradius , minimal annulus , minimal width , perimeter

Rights: Copyright © 2007 Departamento de Matemáticas, Universidad Autónoma de Madrid

Vol.23 • No. 3 • Decembar, 2007
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