PreprintCC BY 4.0arXiv
On the inequality μ3 < λ1 for the eigenvalues of the Laplace operator
Abstract
In 1952, Pólya proved the inequality μ2 < λ1 for the eigenvalues of Dirichlet and Neumann problems in domain Ω⊂ ℝd, d ≥ 2. In 2026, Tang and Zhang proved the inequality μ3 < λ1 in the two-dimensional case. We show that μ3 < λ1 for d≥ 3 as well.
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BibTeX
@misc{filonov2026inequality,
title = {{On the inequality $μ_3 < λ_1$ for the eigenvalues of the Laplace operator}},
author = {N. Filonov},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.13180},
eprint = {2610.13180},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.13180},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - On the inequality μ_3 < λ_1 for the eigenvalues of the Laplace operator
AU - N. Filonov
PY - 2026
DA - 2026/10/23
PB - arXiv
DO - 10.48550/arxiv.2610.13180
UR - https://arxiv.org/abs/2610.13180
AB - In 1952, Pólya proved the inequality μ_2 < λ_1 for the eigenvalues of Dirichlet and Neumann problems in domain Ω⊂ ℝ^d, d ≥ 2. In 2026, Tang and Zhang proved the inequality μ_3 < λ_1 in the two-dimensional case. We show that μ_3 < λ_1 for d≥ 3 as well.
ER -