arXiv subjects
Publications and source records attributed to Hyeseon Kim.
We determine infinitesimal $\mathrm{CR}$ automorphisms and stability groups of real hypersurfaces in $\mathbb C^2$ in the case when the hypersurface is nonminimal and of infinite type at the reference point.
Let $Ω$ be a domain in $\mathbb C^n$. Suppose that $\partialΩ$ is smooth pseudoconvex of D'Angelo finite type near a boundary point $ξ_0\in \partialΩ$ and the Levi form has corank at most $1$ at $ξ_0$. Our goal is to show that if the squeezing function $s_Ω(η_j)$ tends to $1$ or the Fridman invariant $h_Ω(η_j)$ tends to $0$ for some sequence $\{η_j\}\subset Ω$ converging to $ξ_0$, then this point must be strongly pseudoconvex.
Given an affine control system $\dot{\mathbf x} = f({\mathbf x}) + \sum_{j=1}^m g_j({\mathbf x}) u_j$ we present an algorithmic process of construction of submanifolds that are invariant under controls assuming that the linear span of $f, g_1, \ldots, g_m$ has constant rank. We use the method of reduction of Pfaffian systems to a largest integrable subsystem and finding the first integrals and the generalized first integrals for the vector fields.
Applying a theorem due to Diederich and Ohsawa on weighted Bergman kernels, we characterize some Hartogs domains by their holomorphic automorphisms.
In this paper we determine the automorphism group of the Fock-Bargmann-Hartogs domain $D_{n,m}$ in $\mathbb{C}^n\times\mathbb{C}^m$ which is defined by the inequality ${\|ζ\|}^2<e^{-μ{\|z\|}^2}$.