Xianghong Gong

activity

20232026

collaborators

5 papers

math.CV2026

A survey on normal forms of real submanifolds with CR singularity

Xianghong Gong, Laurent Stolovitch

We survey results dating back from the seminal works of Bishop and Moser-Webster as well as more recent advances.

math.CV2025

Integrability of Koszul connections on complex vector bundles over domains in $C^{n}$

Xianghong Gong

We study invertible matrix solutions $A$ to the equation $A^{- 1} \partial A = ω^{(0, 1)}$ on a small open subset $U$ of the closure $M$ of a domain $M\subset{\mathbf…

math.CV2025

A homotopy formula for $a_{q}$ domains in complex manifolds

Xianghong Gong, Ziming Shi

We construct a global homotopy formula for $a_{q}$ domains in a complex manifold. The homotopy operators in the formula will gain $1/2$ derivative in Hölder-Zygmund spaces $Λ^{r}$ wh…

math.CV2024

Global Newlander-Nirenberg theorem on domains with finite smooth boundary in complex manifolds

Xianghong Gong, Ziming Shi

Let $M$ be a relatively compact $C^{2}$ domain in a complex manifold $M$ of dimension $n$ . Assume that $H^{1} (M, Θ) = 0$ where $Θ$ is the sheaf of germs of holomorphic tangent…

math.CV2023

Smooth equivalence of families of strongly pseudoconvex domains

Hervé Gaussier, Xianghong Gong, Andrew Zimmer

We establish a smoothness result for families of biholomorphisms between smooth families of strongly pseudoconvex domains, each with trivial biholomorphism group. This is accomplis…

A survey on normal forms of real submanifolds with CR singularity

Integrability of Koszul connections on complex vector bundles over domains in Cn

A homotopy formula for aq​ domains in complex manifolds

Global Newlander-Nirenberg theorem on domains with finite smooth boundary in complex manifolds

Smooth equivalence of families of strongly pseudoconvex domains

Integrability of Koszul connections on complex vector bundles over domains in $C^{n}$

A homotopy formula for $a_{q}$ domains in complex manifolds