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In \cite{CMS}, Chen-Ma-Salani established the strict convexity of spacetimelevel sets of solutions to heat equation in convex rings, using the constantrank theorem and a deformation method. In this paper, we generalize theconstant rank theorem in \cite{CMS} to fully nonlinear parabolic equations,that is, establish the corresponding microscopic spacetime convexity principlesof spacetime level sets. In fact, the results hold for fully nonlinearparabolic equations under a general structural condition, including the$p$-Laplacian parabolic equations ($p >1$) and some mean curvature typeparabolic equations.

On the microscopic spacetime convexity principle of fully nonlinear parabolic equations II: Spacetime quasiconcave solutions