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