Rigidity of flat surfaces under the boundary measure
  Consider a closed marked flat surface $S$ of genus $g\geq 2$ and area 1 and its universal covering $\tilde{S}$. We show that the measure class of the Hausdorff measure of the Gromov boundary of $\tilde{S}$ uniquely determines $S$. 
Klaus Dankwart
math.DS math.DG