Title: On the PPW Conjecture for Hopf-Symmetric Sets in Non-compact Rank One Symmetric Spaces   

Speaker:Yusen Xia (University of California, Santa Barbara)

Time: Wednesday, July 2, 2025 ,15:30-16:30

Venue: Room 3A02, Building No. 37, Wushan Campus

Abstract: 

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.