an:02100242
Zbl 1074.52004
Hern??ndez Cifre, Mar??a A.; Salinas, Guillermo; Segura Gomis, Salvador
Two optimization problems for convex bodies in the \(n\)-dimensional space
EN
Beitr. Algebra Geom. 45, No. 2, 549-555 (2004).
00109660
2004
j
52A40 52A20 52A38
convex body; volume; surface area; minimal width; diameter; circumradius; inradius
The paper gives upper estimates of the volume and the surface area of \(n\)-dimensional convex bodies with given diameter \(d\) and minimal width \(\omega\). The estimates are attained for the symmetric slice \(S(\omega, d)\) of the ball of diameter \(d\) bounded by two parallel hyperplanes at distance apart \(\omega\). As a corollary, the volume and the surface area of \(n\)-dimensional convex bodies with given circumradius \(R\) and minimal width \(\omega\) are estimated from above. These estimates are attained for the slice \(S(\omega, 2R)\).
Marek Lassak (Bydgoszcz)