A Minimal Value Problem and the Prescribed $\sigma_2$ Curvature Measure Problem

Abstract

In this paper, we consider a minimal value problem and obtain an algebraic inequality. As an application, we prove the $C^2$ a priori estimate for a class of prescribed $\sigma_2$ curvature measure equations, which generalizes the results of the $\sigma_2$ case in Guan-Li-Li\cite{GLL11} by a different method.