学术报告报告题目: On the PPW Conjecture for Hopf-Symmetric Sets in Non-compact Rank One Symmetric Spaces
报 告 人: Yusen Xia (University of California, Santa Barbara)
报告时间: 2025年7月2日（星期三） 下午15:30-16:15
报告地点：37号楼3A02
邀 请 人：温焕尧 教授
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数学学院
2025年7月1日
报告摘要：
Comparison results on eigenvalues of Laplace Operators are important and interesting topics in spectral geometry. In the 1990s Asbaugh and Benguria proved the Payne-Pólya-Weinberger (PPW) inequality, which says balls maximize the ratio of the first two Dirichlet eigenvalues of a bounded domain in Rn. A reformulated version has been proved in the hemisphere and also hyperbolic space. Recently we generalize the PPW inequality to Hopf symmetric sets in non-compact rank one symmetric spaces.
报告人简介：
Yusen Xia is a 4th year PhD student at Mathematics Department, University of California, Santa Barabra. He got his BSc in Mathematics degree (with First Class honors) from Hong Kong University of Science & Technology (HKUST) in 2021. His research interests include eigenvalues problems in differential geometry and manifolds with Ricci curvature lower bounds.