A note on interior curvature estimates for strictly convex solutions to the equation of prescribed curvature quotient

Abstract

In this note, we prove a priori interior curvature bounds for strictly convex solutions to elliptic Weingarten curvature quotient equations. The proof does not employ the advanced methods involving integral estimates or compactness arguments. Instead, it relies on a concavity inequality for the equation operator and a novel choice of the auxiliary function to carry out an elementary maximum-principle argument. Interior curvature estimates for strictly convex solutions to the special Lagrangian curvature equation in low dimensions also follow as a consequence.