Speaker：Guojian Huang (Shenzhen University)

Time：2025-12-4 14:30

Location：Conference Room S204 at Experiment Building at Haiyun Campus

Abstract:

Let $X$ be an irreducible Hermitian symmetric space of noncompact type. By Harish-Chandra realisation, $X\cong \Omega$ is realised as an irreducible bounded domain $\Omega\subset \mathbb{C}^n$. Let $M$ be the compact dual of $X$. Since $M$ is Fano and of Picard number one, there is a natural notion of minimal rational curves on $M$. We study the minimal rational curves intersecting $\Omega$.

Consider a point $b\in Reg(\partial \Omega)$. For the cone of minimal rational curves $\mathcal{V}_b$, Mok showed that the image $V_b:=\Omega\cap \mathcal{V}_b$ is holomorphically isometric to a complex unit ball.

In this talk, we briefly describe how such holomorphic isometry is obtained. Moreover, we construct from it a projection map $c_\Phi: \Omega\rightarrow \Phi$, where $\Phi\subset Reg(\partial\Omega)$ is a boundary component of $\partial \Omega$. Via the study of the moduli of all such projection maps, we recover a special case of the classical Fatou's Theorem on bounded symmetric domain, together with some fine structures related to the geometry of minimal rational curves. If time permit, we also mention some applications to rigidity problems in relation to Carath\'eodory geometry.