info:eu-repo/semantics/article
The Minimal Volume of Simplices Containing a Convex Body
Fecha
2019-01Registro en:
Galicer, Daniel Eric; Merzbacher, Diego Mariano; Pinasco, Damian; The Minimal Volume of Simplices Containing a Convex Body; Springer; The Journal Of Geometric Analysis; 29; 1; 1-2019; 717-732
1050-6926
CONICET Digital
CONICET
Autor
Galicer, Daniel Eric
Merzbacher, Diego Mariano
Pinasco, Damian
Resumen
Let K⊂ Rn be a convex body with barycenter at the origin. We show there is a simplex S⊂ K having also barycenter at the origin such that (vol(S)vol(K))1/n≥cn, where c> 0 is an absolute constant. This is achieved using stochastic geometric techniques. Precisely, if K is in isotropic position, we present a method to find centered simplices verifying the above bound that works with extremely high probability. By duality, given a convex body K⊂ Rn we show there is a simplex S enclosing Kwith the same barycenter such that(vol(S)vol(K))1/n≤dn,for some absolute constant d> 0. Up to the constant, the estimate cannot be lessened.