  Quantum gravity effects modify the Heisenberg's uncertainty principle to a
generalized uncertainty principle (GUP). Earlier work showed that the
GUP-induced corrections to the Schr\"odinger equation, when applied to a
non-relativistic particle in a one-dimensional box, led to the quantization of
length. Similarly, corrections to the Klein-Gordon and the Dirac equations,
gave rise to length, area and volume quantizations. These results suggest a
fundamental granular structure of space. In this work, it is investigated how
spacetime curvature and gravity might influence this discreteness of space. In
particular, by adding a weak gravitational background field to the above three
quantum equations, it is shown that quantization of lengths, areas and volumes
continue to hold. However, it should be noted that the nature of this new
quantization is quite complex and under proper limits, it reduces to cases
without gravity. These results suggest that quantum gravity effects are
universal.
