Xiang He

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math.SP2025

PÃ³lya's conjecture for thin products

Xiang He, Zuoqin Wang

Let $I^c ◯ \subset R^{d}$ be a bounded Euclidean domain. According to the famous Weyl law, both its Dirichlet eigenvalue $I^»_{k} (I^c ◯)$ and its Neumann eigenvalue $I^¼_{k} (I^c ◯)$ have the…

math.SP2025

Prescription of the Robin spectrum

Xiang He, Zuoqin Wang

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