  Very recently, a new concept called multiplicative differential and the
corresponding $c$-differential uniformity were introduced by Ellingsen et al. A
function $F(x)$ over finite field $\mathrm{GF}(p^n)$ to itself is called
$c$-differential uniformity $\delta$, or equivalent, $F(x)$ is differentially
$(c,\delta)$ uniform, when the maximum number of solutions
$x\in\mathrm{GF}(p^n)$ of $F(x+a)-F(cx)=b$, $a,b,c\in\mathrm{GF}(p^n)$,
$c\neq1$ if $a=0$, is equal to $\delta$. The objective of this paper is to
study the $-1$-differential uniformity of ternary APN power functions
$F(x)=x^d$ over $\mathrm{GF}(3^n)$. We obtain ternary power functions with low
$-1$-differential uniformity, and some of them are almost perfect
$-1$-nonlinear.
