Year: 2026
Type: preprint
Abstract: We prove the strict Pólya inequality for Neumann eigenvalues of spherical shells in every dimension $d\ge2$, for every radius ratio and every positive energy. The proof also covers balls. For shells, the excess over the leading Weyl term has a positive lower bound depending only on dimension. Above explicit frequency thresholds independent of the radius ratio, we obtain a surplus of boundary order. These estimates remain uniform as the hole shrinks or the shell becomes thin. We compare weighted sampling errors for inverse radial actions while retaining the removed volume exactly. The proof is entirely analytic and requires no computer-assisted verification.
Source: arXiv (Cornell University)
Author: Li, Yutian
Institution: Nanfang College Guangzhou
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G3001884546
OpenAlex ID: W7223411965