The Gromov-Lawson-Rosenberg conjecture for cocompact Fuchsian groups
  We prove the Gromov-Lawson-Rosenberg conjecture for cocompact Fuchsian groups, thereby giving necessary and sufficient conditions for a closed spin manifold of dimension greater than four with fundamental group cocompact Fuchsian to admit a metric of positive scalar curvature. 
James F. Davis and Kimberly Pearson