Aleksandrov-Fenchel inequalities for unitary valuations of degree 2 and   3
  We extend the classical Aleksandrov-Fenchel inequality for mixed volumes to functionals arising naturally in hermitian integral geometry. As a consequence, we obtain Brunn-Minkowski and isoperimetric inequalities for hermitian quermassintegrals. 
Judit Abardia and Thomas Wannerer
math.DG