Mixed volumes and connected variational problems
Nina Mikhailovna Ivochkina · Project Euclid (Cornell University) · 1990
The recent achievements concerning $m$-curvature equations gave a new point of view to the geometrical theory of mixed volumes of convex bodies which was developed by A.D. Aleksandrov in I938-I940. A principal goal of this paper is to pose corresponding variational problems correctly and to formulate sufficient conditions for the existence of minimizers.