Bellman VS Beurling: sharp estimates of uniform convexity for $L^p$   spaces
  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. 
Paata Ivanisvili, Dmitriy M. Stolyarov, Pavel B. Zatitskiy
math.CA math.DG math.FA