  After establishing suitable notions of stability and Chern classes for
singular pairs, we use K\"ahler-Einstein metrics with conical and cuspidal
singularities to prove the slope semistability of orbifold tangent sheaves of
minimal log-canonical pairs of log general type. We then proceed to prove the
Miyaoka-Yau inequality for all minimal pairs with standard coefficients. Our
result in particular provides an alternative proof of the Abundance theorem for
threefolds that is independent of positivity results for tangent sheaves.
