This is an announcement for the paper "GL(n) contravariant Minkowski valuations" by Franz E. Schuster and Thomas Wannerer. Abstract: A complete classification of all continuous GL(n) contravariant Minkowski valuations is established. As an application we present a family of sharp isoperimetric inequalities for such valuations which generalize the classical Petty projection inequality. Archive classification: math.MG math.DG math.FA Mathematics Subject Classification: 52B45, 52A20, 52A40 Citation: Trans. Amer. Math. Soc. 364 (2012), 815–826 Submitted from: franz.schuster@tuwien.ac.at The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1207.7256 or http://arXiv.org/abs/1207.7256