Weak Harnack Inequalities for Eigenvalues and the Monotonicity of Hessian's Rank (Analysis in Theory and Applications, 2023)
We study microscopic convexity properties of convex solutions of fully nonlinear parabolic equations under a structural condition introduced by Bian-Guan. We prove weak Harnack inequalities for the eigenvalues of the spatial Hessian of solutions and obtain the monotonicity of Hessian’s rank with respect to time.