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.
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.