Monotonicity and Limiting Behavior of Einstein Trees I: Leaf Attachment
组织者
演讲者
时间
2026年06月26日 17:00 至 18:00
地点
A3-4-101
线上
Zoom 204 323 0165
(BIMSA)
摘要
Every finite tree $T$ admits an Einstein metric with Lin–Lu–Yau Ricci curvature $\kappa(T)$. We analyze the asymptotics of $\kappa(T_k)$ for a sequence of trees $\{T_k\}$ generated by repeatedly attaching pendant edges to a designated vertex, establishing the first-order expansion$$\kappa(T_k) = \kappa_\infty - \frac{\alpha}{d+k} + O\left(\frac{1}{(d+k)^2}\right),$$where $\kappa_\infty, d, \alpha \in \mathbb{R}$. If $\alpha \neq 0$, the curvature $\kappa(T_k)$ is eventually strictly monotonic. Consequently, this construction provides rich classes of finite Einstein trees whose curvatures vanish asymptotically.
演讲者介绍
成浩轩，复旦大学数学专业2025级直博研究生，主要研究方向为离散几何分析。目前的研究兴趣包括图上的几何结构、离散曲率理论及其相关的分析问题。曾获复旦大学国家高层次人才培养中心B类资助。