  We characterize the minimal time horizon over which any equity market with $d
\geq 2$ stocks and sufficient intrinsic volatility admits relative arbitrage
with respect to the market portfolio. If $d \in \{2,3\}$, the minimal time
horizon can be computed explicitly, its value being zero if $d=2$ and
$\sqrt{3}/(2\pi)$ if $d=3$. If $d \geq 4$, the minimal time horizon can be
characterized via the arrival time function of a geometric flow of the unit
simplex in $\mathbb R^d$ that we call the minimum curvature flow.
