Open Access Research

On the quermassintegrals of convex bodies

Chang Jian Zhao1* and Wing Sum Cheung2

Author Affiliations

1 Department of Mathematics, China Jiliang University, Hangzhou, 310018, P.R. China

2 Department of Mathematics, The University of Hong Kong, Pokfulam Road, Hong Kong, P.R. China

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Journal of Inequalities and Applications 2013, 2013:264  doi:10.1186/1029-242X-2013-264

Published: 27 May 2013

Abstract

The well-known question for quermassintegrals is the following: For which values of <a onClick="popup('http://www.journalofinequalitiesandapplications.com/content/2013/1/264/mathml/M1','MathML',630,470);return false;" target="_blank" href="http://www.journalofinequalitiesandapplications.com/content/2013/1/264/mathml/M1">View MathML</a> and every pair of convex bodies K and L, is it true that

<a onClick="popup('http://www.journalofinequalitiesandapplications.com/content/2013/1/264/mathml/M2','MathML',630,470);return false;" target="_blank" href="http://www.journalofinequalitiesandapplications.com/content/2013/1/264/mathml/M2">View MathML</a>

In 2003, the inequality was proved if and only if <a onClick="popup('http://www.journalofinequalitiesandapplications.com/content/2013/1/264/mathml/M3','MathML',630,470);return false;" target="_blank" href="http://www.journalofinequalitiesandapplications.com/content/2013/1/264/mathml/M3">View MathML</a> or <a onClick="popup('http://www.journalofinequalitiesandapplications.com/content/2013/1/264/mathml/M4','MathML',630,470);return false;" target="_blank" href="http://www.journalofinequalitiesandapplications.com/content/2013/1/264/mathml/M4">View MathML</a>. Following the problem, in the paper, we prove some interrelated results for the quermassintegrals of a convex body.

MSC: 26D15, 52A30.

Keywords:
symmetric function; convex body; quermassintegral