Journal of Inequalities and Applications
Volume 2010 (2010), Article ID 697954, 18 pages
doi:10.1155/2010/697954
Research Article

On Isoperimetric Inequalities in Minkowski Spaces

Horst Martini1 and Zokhrab Mustafaev2

1Faculty of Mathematics, University of Technology Chemnitz, 09107 Chemnitz, Germany
2Department of Mathematics, University of Houston-Clear Lake, Houston, TX 77058, USA

Received 11 July 2009; Revised 2 December 2009; Accepted 4 March 2010

Academic Editor: Ulrich Abel

Copyright © 2010 Horst Martini and Zokhrab Mustafaev. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The purpose of this expository paper is to collect some (mainly recent) inequalities, conjectures, and open questions closely related to isoperimetric problems in real, finite-dimensional Banach spaces (= Minkowski spaces). We will also show that, in a way, Steiner symmetrization could be used as a useful tool to prove Petty's conjectured projection inequality.