Firey-Shephard problems for homogeneous measures
type: Item
instance of: scholarly article
title: Firey-Shephard problems for homogeneous measures
zbMATH Open document ID: 1381.52008
author: Denghui Wu
published in: Journal of Mathematical Analysis and Applications
publication date: 2017-11-02T00:00:00Z
review text: In recent years, the Brunn-Minkowski theory and its dual have been developed for general measures. A natural question is whether one can expect an affirmative answer to the analogue Firey-Shephard problem for measures. The present paper is concerned with the Firey-Shephard problem for general measures. To this end, some notions of the \(L_p\)-Brunn-Minkowski theory for general measures are introduced, and in particular, the concept of Firey-projection function for a \(\mu\)-measure, which is an extension of the \(L_p\)-projection body. The Firey-Shephard problem for measures is considered and is connected to the \(L^p\)-projection body. Using this connection, a negative answer to the Firey-Shephard problem for homogeneous measures for all \(p>1\), \(p\neq n\) and \(n\geq 2\) is given. A measure comparison theorem is put forward.
Mathematics Subject Classification ID: 52A20
zbMATH DE Number: 6802301
zbMATH Keywords: Fourier transform
zbMATH Keywords: convex bodies
zbMATH Keywords: measures
zbMATH Keywords: Firey-Shephard problem
zbMATH Keywords: \(L_p\)-projection body
reviewed by: A. R. Alimov
MaRDI profile type: Publication
full work available at URL: j.jmaa.2017.08.054
OpenAlex ID: W2753122391
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DOI: 10.1016/J.JMAA.2017.08.054
description: scientific article; zbMATH DE number 6802301