Year: 2026
Type: article
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.
Source: Journal of Geometric Analysis
Author: Yusen Xia
Institution: University of California, Santa Barbara
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,290
Award: G5298098222
OpenAlex ID: W7126236040