This is an announcement for the paper "A remark on the Mahler conjecture: local minimality of the unit cube" by Fedor Nazarov, Fedor Petrov, Dmitry Ryabogin, and Artem Zvavitch. Abstract: We prove that the unit cube $B^n_{\infty}$ is a strict local minimizer for the Mahler volume product $vol_n(K)vol_n(K^*)$ in the class of origin symmetric convex bodies endowed with the Banach-Mazur distance. Archive classification: math.FA Mathematics Subject Classification: 52A15, 52A21 The source file(s), MahlerNPRZ_May_3.tex: 26147 bytes, is(are) stored in gzipped form as 0905.0867.gz with size 9kb. The corresponding postcript file has gzipped size 89kb. Submitted from: zvavitch@math.kent.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0905.0867 or http://arXiv.org/abs/0905.0867 or by email in unzipped form by transmitting an empty message with subject line uget 0905.0867 or in gzipped form by using subject line get 0905.0867 to: math@arXiv.org.