  Let $\mathbf{G}:=(G_1, G_2, G_3)$ be a triple of graphs on a common vertex
set $V$ of size $n$. A rainbow triangle in $\mathbf{G}$ is a triple of edges
$(e_1, e_2, e_3)$ with $e_i\in G_i$ for each $i$ and $\{e_1, e_2, e_3\}$
forming a triangle in $V$. In this paper we consider the following question:
what triples of minimum degree conditions $(\delta(G_1), \delta(G_2),
\delta(G_3))$ guarantee the existence of a rainbow triangle? This may be seen
as a minimum degree version of a problem of Aharoni, DeVos, de la Maza,
Montejanos and \v{S}\'amal on density conditions for rainbow triangles, which
was recently resolved by the authors. We establish that the extremal behaviour
in the minimum degree setting differs strikingly from that seen in the density
setting, with discrete jumps as opposed to continuous transitions. Our work
leaves a number of natural questions open, which we discuss.
