PreprintCC0arXiv
Minimizers of Laplace eigenvalues under a lower curvature bound
Abstract
We prove a sharp comparison, with Obata-type rigidity, for all Neumann eigenvalues of one-dimensional CD(1,2) spaces against the Legendre model, under a convexity condition on the density. It follows that minimizers of the k-th Laplace eigenvalue among closed surfaces of Gaussian curvature at least $1$ cannot collapse in the measured Gromov-Hausdorff completion, for every k≥2. We also give a variational proof that smooth minimizers are round.
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BibTeX
@misc{tiwari2026minimizers,
title = {{Minimizers of Laplace eigenvalues under a lower curvature bound}},
author = {Aditya Tiwari},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.02808},
eprint = {2609.02808},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.02808},
note = {CC0},
}
RIS
TY - UNPB
TI - Minimizers of Laplace eigenvalues under a lower curvature bound
AU - Aditya Tiwari
PY - 2026
DA - 2026/09/02
PB - arXiv
DO - 10.48550/arxiv.2609.02808
UR - https://arxiv.org/abs/2609.02808
AB - We prove a sharp comparison, with Obata-type rigidity, for all Neumann eigenvalues of one-dimensional CD(1,2) spaces against the Legendre model, under a convexity condition on the density. It follows that minimizers of the k-th Laplace eigenvalue among closed surfaces of Gaussian curvature at least $1$ cannot collapse in the measured Gromov-Hausdorff completion, for every k≥2. We also give a variational proof that smooth minimizers are round.
ER -