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A local expression of the Diederich--Fornaess exponent of complements ofLevi-flat real hypersurfaces is exhibited. This expression describes thecorrespondence between pseudoconvexity of their complements and positivity oftheir normal bundles, which was suggested in a work of Brunella, in aquantitative way. As an application, a connection between theDiederich--Fornaess exponent and the exponent of conformal harmonic measures isdiscussed.

A local expression of the Diederich--Fornaess exponent and the exponent of conformal harmonic measures