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https://www.ias.ac.in/article/fulltext/pmsc/123/04/0577-0586

𝑝-centroid body; star body; spherical integral transformation; 𝑝-cosine transformation.

In this paper, we prove that an origin-symmetric star body is uniquely determined by its 𝑝-centroid body. Furthermore, using spherical harmonics, we establish a result for non-symmetric star bodies. As an application, we show that there is a unique member of $\Gamma_p\langle K \rangle$ characterized by having larger volume than any other member, for all real $p \geq 1$ that are not even natural numbers, where $\Gamma_p\langle K \rangle$ denotes the 𝑝-centroid equivalence class of the star body 𝐾.

Lujun Guo¹ Gangsong Leng¹

1. Department of Mathematics, Shanghai University, Shanghai 200444, China

Published

November 2013

Manuscript received

20 June 2012

Manuscript revised

4 October 2012