PreprintCC BY 4.0arXiv
Centro-affine spectral geometry of polytopes
Abstract
In this paper, we develop a polyhedral version of Milman's centro-affine spectral framework for full-dimensional origin-symmetric polytopes. A weighted graph Laplacian on the facets plays the role of the smooth centro-affine Laplacian. For n≥ 3, we prove that its first nonconstant even eigenvalue satisfies λ1,e(P)≥ n−1+1/(n−1) whenever P is a local minimizer of λ1,e among origin-symmetric polytopes with the same facet normals, but not necessarily the same normal fan.
Related
BibTeX
@misc{hu2026centroaffine,
title = {{Centro-affine spectral geometry of polytopes}},
author = {Yingxiang Hu and Mohammad N. Ivaki},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.21670},
eprint = {2609.21670},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.21670},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Centro-affine spectral geometry of polytopes
AU - Yingxiang Hu
AU - Mohammad N. Ivaki
PY - 2026
DA - 2026/09/18
PB - arXiv
DO - 10.48550/arxiv.2609.21670
UR - https://arxiv.org/abs/2609.21670
AB - In this paper, we develop a polyhedral version of Milman's centro-affine spectral framework for full-dimensional origin-symmetric polytopes. A weighted graph Laplacian on the facets plays the role of the smooth centro-affine Laplacian. For n≥ 3, we prove that its first nonconstant even eigenvalue satisfies λ_1,e(P)≥ n−1+1/(n−1) whenever P is a local minimizer of λ_1,e among origin-symmetric polytopes with the same facet normals, but not necessarily the same normal fan.
ER -