发表机构
Dalian University of Technology（大连理工大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明欧几里得圆环的所有Neumann特征值满足Pólya不等式，通过径向作用恒等式与变分界结合，并借助区间证书验证，推广至环形乘积与扇形。
AI 中文摘要
我们证明了每个欧几里得圆环的每个Neumann特征值都满足Pólya不等式。该证明通过径向作用恒等式保留了精确的Weyl面积项，并将变分界与均匀的Bessel相位和角求和估计相结合。当宽度不超过内半径的四分之一时，证明完全是解析的。对于任意半径，显式的高频和小孔界将问题归结为一个紧致参数区域，该区域通过在整个参数矩形上有效的精确有理数和向外区间证书进行验证。已建立的传递原理给出了环形乘积和全等环形扇形的Neumann不等式。
英文摘要
We prove Pólya's inequality for every Neumann eigenvalue of every Euclidean circular annulus. The proof preserves the exact Weyl area term through a radial action identity and combines variational bounds with uniform Bessel-phase and angular-sum estimates. It is entirely analytic when the width is at most one quarter of the inner radius. For arbitrary radii, explicit high-frequency and small-hole bounds reduce the problem to a compact parameter region, which is verified by exact rational and outward interval certificates valid on whole parameter rectangles. Established transfer principles yield the Neumann inequality for annular products and congruent annular sectors.
