Higgs sheaves on singular spaces and the Miyaoka-Yau Inequality for minimal varieties of general type

We establish the Miyaoka-Yau inequality for the tangent sheaf of any minimal, complex, projective variety X of general type, with only klt singularities. In the case of equality, we prove that the canonical model of X has only quotient singularities and is uniformized by the unit ball. Joint with Greb, Peternell, Taji.