A local expression of the Diederich--Fornaess exponent and the exponent   of conformal harmonic measures
  A local expression of the Diederich--Fornaess exponent of complements of Levi-flat real hypersurfaces is exhibited. This expression describes the correspondence between pseudoconvexity of their complements and positivity of their normal bundles, which was suggested in a work of Brunella, in a quantitative way. As an application, a connection between the Diederich--Fornaess exponent and the exponent of conformal harmonic measures is discussed. 
Masanori Adachi
math.CV math.DS