Liouville property and regularity of a Hessian quotient equation

Abstract

We are concerned with properties of (convex) solutions to the Hessian quotient equation S n,k ( D 2 u ) = φ, 1 ≤ k < n . As our first main result we prove some regularity of strong solutions, while the second states that for φ ≡ 1 an entire convex solution with a quadratic growth bound must be a quadratic polynomial.