Renjin Jiang

collaborators

3 papers

math.SP2026

New Qualitative and Quantitative Estimates for Neumann Eigenvalues toward Pólya's Conjecture

Xiang He, Renjin Jiang, Fanghua Lin +1

We introduce the Enhanced Neumann Pólya inequality, which is stronger than Pólya's conjecture, and verify it for many classes of domains, including strip-tiling domains, Euclidean…

math.SP2025

Improved Berezin-Li-Yau inequality and Kröger inequality and consequences

Zaihui Gan, Renjin Jiang, Fanghua Lin

We provide quantitative improvements to the Berezin-Li-Yau inequality and the Kröger inequality, in $R^{n}$ , $n \geq 2$ . The improvement on Kröger's inequality resolves an ope…

math.SP2025

Pólya's conjecture up to $ε$ -loss and quantitative estimates for the remainder of Weyl's law

Renjin Jiang, Fanghua Lin

Let $Ω \subset R^{n}$ be a bounded Lipschitz domain. For any $ε \in (0, 1)$ we show that for any Dirichlet eigenvalue $λ_{k} (Ω) > Λ (ε, Ω)$ , it holds \begin{align*} k&\le (1+ε)\frac{|…

New Qualitative and Quantitative Estimates for Neumann Eigenvalues toward Pólya's Conjecture

Improved Berezin-Li-Yau inequality and Kröger inequality and consequences

Pólya's conjecture up to ε-loss and quantitative estimates for the remainder of Weyl's law

Pólya's conjecture up to $ε$ -loss and quantitative estimates for the remainder of Weyl's law