This is an announcement for the paper "On improvement of the concavity of convex measures" by Arnaud Marsiglietti. Abstract: We prove that a general class of measures, which includes $\log$-concave measures, are $\frac{1}{n}$-concave in the terminology of Borell under additional assumptions on the measure or on the sets, such as symmetries. This generalizes results of Gardner and Zvavitch. Archive classification: math.FA Submitted from: arnaud.marsiglietti@univ-mlv.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1403.7643 or http://arXiv.org/abs/1403.7643