On a family of analytic discs attached to a real submanifold $M\subset\mathbb{C}^{N+1}$

Flattening of CR singular points and analyticity of the local hull of holomorphy I

“…Theorem 1.3 is equivalent to Theorem 1.4 by a classical result of Cartan which states that a real analytic hypersurface is Levi-flat if and only if it can be transformed locally to an open piece of the standard Levi-flat hyperplane defined by ℑw = 0. When all Bishop invariants at p are elliptic, we mention that Theorem 1.4 can also be derived by combining the results obtained in Dolbeault-Tomassini-Zaitsev [DTZ1-2] and the work in a very recent preprint by Burcea [Bur2] with a different approach. (The work in Dolbeault-Tomassini-Zaitsev [DTZ1-2] contains other very nice global results.)…”

“…Finally, We also mention a recent preprint [Bur2] for some generalization of the work in Kenig-Webster [KW] and Huang-Krantz [HK].…”

“…(The work in Dolbeault-Tomassini-Zaitsev [DTZ1-2] contains other very nice global results.) The arguments based on Dolbeault-Tomassini-Zaitsev [DTZ1-2] and Burcea [Bur2] depend strongly on all the ellipticity of Bishop invariants and requires that the CR orbits in M near the CR singular point form a family of compact strongly pseudoconvex manifolds shrinking down to the complex tangent such that the Harvey-Lawson theorem applies. This is certainly not the case even when one non-elliptic Bishop invariant at the CR singular point appears.…”