  We prove that for an unbounded metric space $X$, the minimal character
$m\chi(\check X)$ of a point of the Higson corona $\check X$ of $X$ is equal to
$\mathfrak u$ if $X$ has asymptotically isolated balls and to $\max\{\mathfrak
u,\mathfrak d\}$ otherwise. This implies that under $\mathfrak u<\mathfrak d$ a
metric space $X$ of bounded geometry is coarsely equivalent to the Cantor
macro-cube $2^{<\IN}$ if and only if $\dim(\check X)=0$ and $m\chi(\check
X)=\mathfrak d$. This contrasts with a result of Protasov saying that under CH
the coronas of any two asymptotically zero-dimensional unbounded metric
separable spaces are homeomorphic.
