with bounded curvature on $M \times (0,T]$. Assume that the curvature operator of $g(t)$ is nonnegative for every $t \in (0,T]$.
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For each $(p,t) \in M \times (0,T]$, let $\nabla$, $\Delta$, $R_{ijkl}$, $R_{ij}$, and $R$ denote respectively the Levi-Civita connection, rough Laplacian, Riemann curvature tensor, Ricci tensor, and scalar curvature of $g(t)$ at time $t$. In a local $g(t)$-orthonormal frame, define the tensors
Then for every $(p,t) \in M \times (0,T]$, every skew-symmetric tensor $U \in \Lambda^2T_p^*M$, and every covector $W \in T_p^*M$, the quadratic expression