  In this note we prove convexity, in the sense of Colding-Naber, of the
regular set of solutions to some complex Monge-Ampere equations with conical
singularities along simple normal crossing divisors. In particular, any two
points in the regular set can be joined by a smooth minimal geodesic lying
entirely in the regular set. We show that as a result, the classical theorems
of Myers and Bishop-Gromov extend almost verbatim to this singular setting.
