Xiang He

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20242026

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math.SP2026

New Qualitative and Quantitative Estimates for Neumann Eigenvalues toward Pólya's Conjecture

Xiang He, Renjin Jiang, Fanghua Lin +1

We introduce the Enhanced Neumann Pólya inequality, which is stronger than Pólya's conjecture, and verify it for many classes of domains, including strip-tiling domains, Euclidean…

math.SP2025

Prescription of the Robin spectrum

Xiang He, Zuoqin Wang

Let $M$ be a compact connected smooth manifold with smooth boundary, and let $ρ$ be a positive continuous function on the boundary which is served as the Robin parameter. In this p…

math.SP2024

Pólya's conjecture for thin products

Xiang He, Zuoqin Wang

Let $Ω \subset R^{d}$ be a bounded Euclidean domain. According to the famous Weyl law, both its Dirichlet eigenvalue $λ_{k} (Ω)$ and its Neumann eigenvalue $μ_{k} (Ω)$ have the same…