Aleksandrov-Fenchel inequalities for unitary valuations of degree 2 and 3

Abstract

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.

23 pages

References in corpus (3)

• Integral geometry of complex space forms
• On the inverse Klain map
• The Centro-Affine Hadwiger Theorem