Demonstrates eigenvalue relationships in non-compact symmetric spaces, suggesting broader implications for geometry.
In this paper, we proved that for a bounded Hopf-symmetric domain Ω Ω in a non-compact rank one symmetric space M , the second Dirichlet eigenvalue λ ₂(Ω )≤ λ ₂(B₁) λ 2 ( Ω ) ≤ λ 2 ( B 1 ) where B₁ B 1 is a geodesic ball in M such that λ ₁(Ω ) = λ ₁(B₁) λ 1 ( Ω ) = λ 1 ( B 1 ) . This generalizes the work of Ashbaugh & Benguria, Benguria & Linde for bounded domains in constant curvature spaces.
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Yusen Xia (2026) studied this question.
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