### A microlocal version of Cartan-Grauert's theorem

Tuboids are tube-like domains which have a totally real edge and look asymptotically near the edge as a local tube over a convex cone. For such domains we state an analogue of Cartan’s theorem on the holomorphic convexity of totally real domains in ${\mathbb{R}}^{n}\subset {\u2102}^{n}$.