Do Minkowski averages get progressively more convex?

Matthieu Fradelizi, Mokshay Madiman, Arnaud Marsiglietti, Artem Zvavitch

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

Let us define, for a compact set A⊂Rn, the Minkowski averages of A: We study the monotonicity of the convergence of A(k) towards the convex hull of A, when considering the Hausdorff distance, the volume deficit and a non-convexity index of Schneider as measures of convergence. For the volume deficit, we show that monotonicity fails in general, thus disproving a conjecture of Bobkov, Madiman and Wang. For Schneider's non-convexity index, we prove that a strong form of monotonicity holds, and for the Hausdorff distance, we establish that the sequence is eventually nonincreasing.

Original languageEnglish (US)
Pages (from-to)185-189
Number of pages5
JournalComptes Rendus Mathematique
Volume354
Issue number2
DOIs
StatePublished - Feb 1 2016

Bibliographical note

Publisher Copyright:
© 2015 Académie des sciences.

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