On the PPW Conjecture For Hopf-symmetric Sets In Non-compact Rank One Symmetric Space

Yusen Xia

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arXiv · 2505.18439

On the PPW Conjecture For Hopf-symmetric Sets In Non-compact Rank One Symmetric Space

Yusen Xia

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Abstract

In this paper, we proved that for a bounded Hopf-symmetric domain $\Omega$ in a noncompact rank one symmetric space $M$, the second Dirichlet eigenvalue $\lambda_2 (\Omega) \leq \lambda_2 (B_1)$ where $B_1$ is a geodesic ball in $M$ such that $\lambda_1 (\Omega) =\lambda_1 (B_1)$. This generalizes the work of Ashbaugh & Benguria, Benguria & Linde for bounded domains in constant curvature spaces.

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BibTeX RIS

Yusen Xia. 2025-05-24. On the PPW Conjecture For Hopf-symmetric Sets In Non-compact Rank One Symmetric Space. https://arxiv.org/abs/2505.18439

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