Leo Brauner

Hyperbolicity Beyond Convexity in the Alexandrov-Fenchel Inequality

We establish an Alexandrov--Fenchel type inequality in which one of the reference bodies is replaced by a function whose Hessian satisfies a balancing condition on its eigenvalues, without being required to be positive semidefinite. The proof hinges on a new extension of Alexandrov's inequality for mixed discriminants....