  There exists the duality between normal family theory and value distribution
theory of meromorphic functions, which is called the Bloch principle. Zalcman
formulated a more precise statement on it. In this paper, based on the Zalcman
and Ros work, we comprehend the phenomenon of the trinity among normal family
theory, value distribution theory and minimal surface theory and give a
systematic description to the relationship among the Montel theorem, the
Liuoville theorem and the Bernstein theorem as well as the
Carath\'{e}odory-Montel theorem, the Picard little theorem and the Fujimoto
theorem. We call this phenomenon Bloch-Ros principle. We also generalize the
Bloch-Ros principle to various classes of surfaces, for instance, maxfaces in
the Lorentz-Minkowski $3$-space, improper affine fronts in the affine $3$-space
and flat fronts in the hyperbolic $3$-space. In particular, we give an
effective criterion to determine which properties for meromorphic functions
that play a role of the Gauss maps of these classes of surfaces satisfy the
Gaussian curvature estimate.
