Year: 2026
Type: preprint
Abstract: We prove Laugesen and Siudeja's conjecture on Neumann eigenvalues of isosceles triangles. After multiplication by the squared diameter, the first positive symmetric eigenvalue increases strictly with the apex angle $θ$, while the first antisymmetric eigenvalue decreases strictly up to the equilateral triangle and increases strictly thereafter. \rev{The proof combines a slice-average estimate of directional energies with the explicit equilateral eigenfunction.} A quadratic correction across slices also gives a two-term expansion for every fixed positive spectral index $k$ as $θ\downarrow0$, with relative correction $θ^2/6$ and remainder $O_k(θ^4)$.
Source: arXiv (Cornell University)
Authors: Dai, Guowei, Sun, Yingxin, Zhang, Yong
Institutions: Dalian University of Technology, Jiangsu University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G4772512679, G6844602229
OpenAlex ID: W7214356943