\(L_p\)-bounds on curvature, elliptic estimates and rectifiability of singular sets (Q1598486)

Let \((Y,y_0)\) be a metric space with basepoint which is the Gromov-Hausdorff limit in the category of spaces with basepoints of a sequence of connected Kähler manifolds \((M_i,m_i)\) which satisfy the uniform estimates \(|\text{Ric}(M_i)|\leq -(n-1)\) and \(\text{Vol}(B_1,m_i)\geq v>0\). The author shows that the singular set has complex codimension \(2\). He also gives other results concerning the singular support, when the \(M_i\) are only assumed Riemannian, which are related to \(L^p\) bounds on curvature given by suitable lower bounds on the Ricci curvature.