  We construct a Hilbert space representation of minimum-length deformed
uncertainty relation in presence of extra dimensions. Following this
construction, we study corrections to the gravitational potential (back
reaction on gravity) with the use of correspondingly modified propagator in
presence of two (spatial) extra dimensions. Interestingly enough, for $r
\rightarrow 0$ the gravitational force approaches zero and the horizon for
modified Schwarzschild-Tangherlini space-time disappears when the mass
approaches quantum-gravity energy scale. This result points out to the
existence of zero-temperature black hole remnants in ADD brane-world model.
