Gårding cones and Bellman equations in the theory of Hessian operators and equations

In this work, we continue investigation of algebraic properties of Gårding cones in the space of symmetric matrices. Based on this theory, we propose a new approach to study of fully nonlinear differential operators and second-order partial differential equations. We prove new-type comparison theorems for evolution Hessian operators and establish a relation between Hessian and Bellman equations.