On the PPW Conjecture for Hopf-Symmetric Sets in Non-compact Rank One Symmetric Space
Abstract
Abstract In this paper, we proved that for a bounded Hopf-symmetric domain $$\Omega $$ Ω in a non-compact rank one symmetric space M , the second Dirichlet eigenvalue $$\lambda _2(\Omega )\le \lambda _2(B_1)$$ λ 2 ( Ω ) ≤ λ 2 ( B 1 ) where $$B_1$$ B 1 is a geodesic ball in M such that $$\lambda _1(\Omega ) = \lambda _1(B_1)$$ λ 1 ( Ω ) = λ 1 ( B 1 ) . This generalizes the work of Ashbaugh & Benguria, Benguria & Linde for bounded domains in constant curvature spaces.
Fields of Study & Subjects
Spectral Theory in Mathematical Physics
Geometric Analysis and Curvature Flows
Nonlinear Partial Differential Equations
Publication details
- Journal / source
- Journal of Geometric Analysis
- Volume
- 36
- Issue
- 3
- Publication date
- 30 January 2026
- Language
- EN