Author

Da-Guang Chen

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Preprint Sep 2026

Sharp harmonic-mean inequalities for Neumann and Aharonov--Bohm spectra

We prove sharp two-eigenvalue isoperimetric inequalities for Neumann and Aharonov--Bohm Neumann spectra on surfaces. If $\Omega\subset\mathbb S^2$ is smooth, simply connected and proper, then the harmonic mean of $\mu_2(\Omega)$ and $\mu_3(\Omega)$ is bounded above by the first positive Neumann eigenvalue of the equal-...

Da-Guang Chen, Cheng-Xi Yang · 1 citation · ⚡1

Preprint Jul 2026

Sharp shifted reciprocal sums of Neumann eigenvalues on space forms

Let $\mathbb{M}_\kappa^n$ be the space form of sectional curvature $\kappa\in\{-1,0,1\}$, so that $\mathbb{M}_{-1}^n=\mathbb{H}^n, \mathbb{M}_{0}^n=\mathbb{R}^n, \mathbb{M}_{1}^n=\mathbb{S}^n$. Let $\Omega\subset\mathbb{M}_\kappa^n$ be a nonempty bounded open set with Lipschitz boundary, and assume that $0<|\Omega|<|\m...

Da-Guang Chen, Cheng-Xi Yang · 1 citation · ⚡1