This is an announcement for the paper "Quantitative Borell-Brascamp-Lieb inequalities for compactly power concave functions (and some applications)" by Daria Ghilli and Paolo Salani. Abstract: We strengthen, in two different ways, the so called Borell-Brascamp- Lieb inequality in the class of power concave functions with compact support. As examples of applications we obtain two quantitative versions of the Brunn- Minkowski inequality and of the Urysohn inequality for torsional rigidity. Archive classification: math.AP math.FA Submitted from: ghilli@math.unipd.it The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1502.02810 or http://arXiv.org/abs/1502.02810