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Blaschke-decomposable convex bodies

Authors:	Stefano Campi Andrea Colesanti Paolo Gronchi

Affiliation:	(1) Dipartimento di Matematica Pura e Applicata “G. Vitali”, Università di Modena, Via Campi 213/B, 41100 Modena, Italy;(2) Dipartimento di Matematica “U. Dini”, Firenze, Italy;(3) Istituto di Analisi Globale e Applicazioni (CNR), Firenze, Italy

Abstract:	For a given centred convex bodyK of ℝ,n≥3, let $mathcal{H}_K$ be the class of all convex bodies with the same projection body asK. The question whetherK can be expressed as a Blaschke average of two non-homothetic bodies from $mathcal{H}_K$ is considered. Necessary and sufficient conditions onK to be Blaschke decomposable in $mathcal{H}_K$ are given. The paper provides also a characterization of the bodiesK such that the Blaschke indecomposable bodies in $mathcal{H}_K$ are dense in $mathcal{H}_K$ itself.

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