This is an announcement for the paper "Bellman VS Beurling: sharp estimates of uniform convexity for $L^p$ spaces" by Paata Ivanisvili, Dmitriy M. Stolyarov, and Pavel B. Zatitskiy. Abstract: We obtain the classical Hanner inequalities by the Bellman function method. These inequalities give sharp estimates for the moduli of convexity of Lebesgue spaces. Easy ideas from differential geometry help us to find the Bellman function using neither ``magic guesses'' nor calculations. Archive classification: math.CA math.DG math.FA Remarks: 11 pages Submitted from: dms@pdmi.ras.ru The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1405.6229 or http://arXiv.org/abs/1405.6229