A lower bound for the mass of axisymmetric connected black hole data   sets
  We present a generalisation of the Brill-type proof of positivity of mass for axisymmetric initial data to initial data sets with black hole boundaries. The argument leads to a strictly positive lower bound for the mass of simply connected, connected axisymmetric black hole data sets in terms of the mass of a reference Schwarzschild metric. 
Piotr T. Chru\'sciel and Luc Nguyen
gr-qc