Author

Quanyu Tang

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Preprint Sep 2026

Neumann--Dirichlet eigenvalue comparison at the first Dirichlet threshold in the plane

Let $\Omega\subset\mathbb R^2$ be a bounded connected Lipschitz domain, and let $\{\mu_j(\Omega)\}_{j\geq1}$ and $\{\lambda_j(\Omega)\}_{j\geq1}$ denote the Neumann and Dirichlet Laplacian eigenvalues, respectively, counted with multiplicity. We prove that $$ \mu_3(\Omega)<\lambda_1(\Omega), $$ thereby removing the sim...

Quanyu Tang, Hai-Qi Zhang · 1 citation

Preprint Aug 2026

Three omitted values and non-Blaschke point divisors in half-planes

We construct a real meromorphic function $F$ on $\mathbb C$ such that $F^{-1}(\{0,1,\infty\})\subset\mathbb R$, while $F$ is not of bounded type in either half-plane. More strongly, for every $a\in\widehat{\mathbb C}\setminus\{0,1,\infty\}$, the $a$-point divisor in either half-plane fails the Blaschke condition. Thus...

Quanyu Tang, Boya Cui, Wei He et al. · 0 citations