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Yet another proof is given for a global estimate of the Diederich--Fornaessindex of relatively compact domains with Levi-flat boundary, namely, the indexmust be smaller than or equal to the reciprocal of the dimension of the ambientspace. This proof reveals that this kind of estimate makes sense and holds alsofor abstract compact Levi-flat CR manifolds.

A CR proof for a global estimate of the Diederich--Fornaess index of Levi-flat real hypersurfaces