On the curvature of conic Kaehler-Einstein metrics
  We prove a regularity result for Monge-Amp\`ere equations degenerate along smooth divisor on Kaehler manifolds in Donaldson's spaces of $\beta$-weighted functions. We apply this result to study the curvature of Kaehler metrics with conical singularities along divisors and give a geometric sufficient condition on the divisor for its boundedness. 
Claudio Arezzo, Alberto Della Vedova, Gabriele La Nave
math.DG