Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

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Bull. Korean Math. Soc. 2018; 55(1): 139-148

Online first article August 3, 2017      Printed January 31, 2018

https://doi.org/10.4134/BKMS.b160879

Copyright © The Korean Mathematical Society.

A stability result for p-centroid bodies

Lujun Guo, Gangsong Leng, Youjiang Lin

Henan Normal University, Shanghai University, Chongqing Technology and Business University

Abstract

In this paper, we prove a stability result for $p$-centroid bodies with respect to the Hausdorff distance. As its application, we show that the symmetric convex body is determined by its $p$-centroid body.

Keywords: $p$-centroid body, convex body, spherical integral transformation, $p$-cosine transformation

MSC numbers: 52A20, 52A40