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BIMSA Lecture
BIMSA Lecture
Monotonicity and Limiting Behavior of Einstein Trees I: Leaf Attachment
Monotonicity and Limiting Behavior of Einstein Trees I: Leaf Attachment
Organizer
Speaker
Time
Friday, June 26, 2026 5:00 PM - 6:00 PM
Venue
A3-4-101
Online
Zoom 204 323 0165
(BIMSA)
Abstract
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.
Speaker Intro
Cheng Haoxuan is a Ph.D. student in Mathematics at Fudan University. His research focuses on discrete geometric analysis, with particular interests in geometric structures on graphs, discrete curvature theory, and related analytic problems. He has received the Class B Fellowship from the National High-Level Talent Training Center at Fudan University.