PreprintCC BY 4.0arXiv
A note on the failure of Payne's inequality on manifolds with boundary
Abstract
We show that Payne's conjecture on the comparison between Dirichlet Laplacian eigenvalues and buckling eigenvalues does not hold on flat and hyperbolic cylindrical surfaces and on (round) hemispheres.
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BibTeX
@misc{buoso2026note,
title = {{A note on the failure of Payne's inequality on manifolds with boundary}},
author = {Davide Buoso and Vladimir Lotoreichik},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.20097},
eprint = {2610.20097},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.20097},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A note on the failure of Payne's inequality on manifolds with boundary
AU - Davide Buoso
AU - Vladimir Lotoreichik
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2610.20097
UR - https://arxiv.org/abs/2610.20097
AB - We show that Payne's conjecture on the comparison between Dirichlet Laplacian eigenvalues and buckling eigenvalues does not hold on flat and hyperbolic cylindrical surfaces and on (round) hemispheres.
ER -