Conformal fluctuations do not establish a minimum length
  This paper corrects an earlier work suggesting that the quantum expectation value of the proper length is bounded from below by the Planck length. The original calculation examined fluctuations of the conformal factor of Einstein-Hilbert gravity. However, in Einstein-Hilbert gravity, the conformal factor is not a dynamical field subject to fluctuations. This paper performs the same calculation using the trace anomaly-induced effective action for the conformal factor and finds that, while conformal fluctuations modify the short-distance behavior of the interval, the interval still approaches zero in the coincidence limit. 
Colin Cunliff
gr-qc