Complex geometry and integral representations in the future tube in $\mathbb C^3$

It is shown that the boundary of the future tube in $\mathbb C^3$ cannot be holomorphically reeitified along complex light rays lying on the boundary. From the general Cauchy–Fantappie representation the Cauchy–Bochner, Jost–Lehmann–Dyson, Leray, and other integral representations for holomorphic functions and solutions of the $\bar{\partial}$-equation in the future tube are derived.