  We calculate the lowest-order corrections to the static potential for both
Yang-Mills theory and gluodynamics in curved space-time, in the presence of a
quantum gravity induced minimal length. Our analysis is carried out within
stationary perturbation theory. As a consequence, the potential energy is the
sum of a Yukawa-like potential and a linear potential for gluodynamics in
curved space-time, leading to the confinement of static charges. Interestingly
enough, we obtain that the coefficient of the linear term ("string tension") is
ultraviolet finite. We should highlight the role played by the new quantum of
length in our analysis.
