4 problems

For general convex bodies, the paper seeks analogues of the self-adjoint operators $\mathscr{A}_{\mathcal{C}}$ and an appropriate analogue of the Alexandrov–Fenchel inequality. Fun…

Let $C_1,\ldots,C_{n-2}$ be general convex bodies rather than polytopes, and consider the extremal characterizations established in the paper for the Alexandrov–Fenchel inequality.…

Let $\mathcal{P}=(P_1,\ldots,P_{n-2})$ be polytopes in $\mathbb{R}^n$, let $K,L$ be convex bodies, and let $B$ be the reference body used to define $(B,\mathcal{P})$-extreme normal…

The paper considers the three mechanisms for equality in the Alexandrov–Fenchel inequality given by linear functions, support-based equality, and degenerate pairs; their linear com…