In this talk, I will first define mixed area measures: these are
fundamental geometric measures encoding joint information about
curvature of a family of convex bodies (including also the classical
Gauss and mean curvature). Then we discuss the central Minkowski and
Christoffel problem, as well as their intermediate and mixed versions,
which are about classifying mixed area measures. In the special case
where the convex bodies involved share an axial symmetry, we resolve the
problem completely.
This is joint work with Georg C. Hofstätter and Oscar Ortega-Moreno
