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Conformal Eigenvalues on Tori

组织者

深谷賢治 , 杨琳 , 塞巴斯蒂安·赫勒 , 河井公大朗 , Enric Sole Farre

演讲者

Kang Fan

时间

2026年04月14日 14:30 至 16:30

地点

A3-4-301

线上

Zoom 293 812 9202 (BIMSA)

摘要

In this talk, we discuss extremal problems for Laplace–Beltrami eigenvalues on unit-area tori. We first review Berger’s isoperimetric problem for the first eigenvalue and present a new proof using the conformal area method and Bryant’s results on tori. We next turn to the second eigenvalue. Building on general bounds for $\lambda_2$ on surfaces due to Karpukhin–Stern and Eddaoudi–Girouard, we obtain an improved upper bound for tori in a fixed conformal class. Our result improves previous estimates and provides further evidence for the Kao–Lai–Osting conjecture. This work is joint with Zhenlei Zhang.