  We formulate generalized uncertainty relations in a crystal-like universe
whose lattice spacing is of the order of Planck length -- "world crystal". In
the particular case when energies lie near the border of the Brillouin zone,
i.e., for Planckian energies, the uncertainty relation for position and momenta
does not pose any lower bound on involved uncertainties. We apply our results
to micro black holes physics, where we derive a new mass-temperature relation
for Schwarzschild micro black holes. In contrast to standard results based on
Heisenberg and stringy uncertainty relations, our mass-temperature formula
predicts both a finite Hawking's temperature and a zero rest-mass remnant at
the end of the micro black hole evaporation. We also briefly mention some
connections of the world crystal paradigm with 't Hooft's quantization and
double special relativity.
