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We characterize the Diederich-Fornaess index and the Steinness index in terms of a special 1-form, which we call DAngelo 1-form. We then prove that the Diederich-Fornaess and Steinness indices are invariant under CR-diffeomorphisms by showing CR-invariance of DAngelo 1-forms.
We introduce the concept of Steinness index related to the Stein neighborhood basis. We then show several results: (1) The existence of Steinness index is equivalent to that of strong Stein neighborhood basis. (2) On the Diederich-Forn{ae}ss worm dom
We propose the concept of Diederich--Forn{ae}ss and Steinness indices on compact pseudoconvex CR manifolds of hypersurface type in terms of the DAngelo 1-form. When the CR manifold bounds a domain in a complex manifold, under certain additional non-d
In this paper, we prove the semi-continuity theorem of Diederich-Forn{ae}ss index and Steinness index under a smooth deformation of pseudoconvex domains in Stein manifolds.
In this paper we characterize sums of CR functions from competing CR structures in two scenarios. In one scenario the structures are conjugate and we are adding to the theory of pluriharmonic boundary values. In the second scenario the structures are
A smooth, strongly $mathbb{C}$-convex, real hypersurface $S$ in $mathbb{CP}^n$ admits a projective dual CR structure in addition to the standard CR structure. Given a smooth function $u$ on $S$, we provide characterizations for when $u$ can be decomp