  In the minimal surface theory, the Krust theorem asserts that if a minimal
surface in the Euclidean 3-space $\mathbb{E}^3$ is the graph of a function over
a convex domain, then each surface of its associated family is also a graph.
The same is true for maximal surfaces in the Minkowski 3-space $\mathbb{L}^3$.
  In this article, we introduce a new deformation family that continuously
connects minimal surfaces in $\mathbb{E}^3$ and maximal surfaces in
$\mathbb{L}^3$, and prove a Krust-type theorem for this deformation family.
This result induces Krust-type theorems for various important deformation
families containing the associated family and the L\'opez-Ros deformation.
  Furthermore, minimal surfaces in the isotropic 3-space $\mathbb{I}^3$ appear
in the middle of the above deformation family. We also prove another type of
Krust's theorem for this family, which implies that the graphness of such
minimal surfaces in $\mathbb{I}^3$ strongly affects the graphness of deformed
surfaces.
  The results are proved based on the recent progress of planar harmonic
mapping theory.
