  Let $u$ be a non-negative super-solution to a $1$-dimensional singular
parabolic equation of $p$-Laplacian type ($1<p<2$). If $u$ is bounded below on
a time-segment $\{y\}\times(0,T]$ by a positive number $M$, then it has a
power-like decay of order $\frac p{2-p}$ with respect to the space variable $x$
in $\mathbb R\times[T/2,T]$. This fact, stated quantitatively in Proposition
1.1, is a "sidewise spreading of positivity" of solutions to such singular
equations, and can be considered as a form of Harnack inequality. The proof of
such an effect is based on geometrical ideas.
