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

TL;DR

This paper provides a new proof for a global estimate of the Diederich--Fornaess index in Levi-flat domains, extending the result to abstract compact Levi-flat CR manifolds, and clarifying its broader applicability.

Contribution

It introduces a novel proof technique for the index estimate and demonstrates its validity for abstract Levi-flat CR manifolds, broadening the scope of previous results.

Findings

The Diederich--Fornaess index is bounded above by the reciprocal of the ambient space's dimension.

The estimate applies to both relatively compact domains and abstract compact Levi-flat CR manifolds.

The new proof confirms the estimate's validity in a more general setting.

Abstract

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