Convexity of solutions and Brunn-Minkowski inequalities for Hessian   equations in $\R^3$
  By using Minkowski addition of convex functions, we prove convexity and rearrangement properties of solutions to some Hessian equations in $\R^3$ and Brunn-Minkowski and isoperimetric inequalities for related functionals. 
Paolo Salani
math.AP