Conformal Eigenvalues on Tori
Organizers
Speaker
Kang Fan
Time
Tuesday, April 14, 2026 2:30 PM - 4:30 PM
Venue
A3-4-301
Online
Zoom 293 812 9202
(BIMSA)
Abstract
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.