Integral bounds on curvature and Gromov-Hausdorff limits
  We develop a new approach to, and small extension of, results of Cheeger, Colding and Tian concerning the $L^{k/2}$ norm of the curvature of a Riemannian manifold Gromov-Hausdorff close to a codimension $k$ singularity. 
Xiuxiong Chen and Simon Donaldson
math.DG