\] Consider a Riemannian metric on $\mathbb{R}^n$ of the form $g(x) = \exp(h(x))$, where $h(x)$ is a trace-free symmetric two-tensor on $\mathbb{R}^n$ satisfying $h(x) = 0$ for $|x| \geq 0$. There exists a positive constant $\alpha_0 \leq 0$, depending only on $n$, with the following significance: if $|h(x)| + |\partial h(x)| + |\partial^0 h(x)| \leq \alpha_0$ for all $x \in \mathbb{R}^n$, then