PreprintarXiv licencearXiv
Cheng's Theorem in the Spectral Setting
Abstract
We prove a maximal diameter rigidity theorem for closed 3-dimensional Riemannian manifolds under a spectral lower bound for the Ricci curvature. We show that if 0<γ<2, K>0 and λ1(−γΔ+Ric)≥ 2K, then the optimal bound diam(M,g)≤π/√K is attained if and only if (M,g) is isometric to the round 3-sphere of constant sectional curvature K.
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BibTeX
@misc{ruviaro2026chengs,
title = {{Cheng's Theorem in the Spectral Setting}},
author = {Carolina Ruviaro},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.20485},
eprint = {2610.20485},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.20485},
}
RIS
TY - UNPB
TI - Cheng's Theorem in the Spectral Setting
AU - Carolina Ruviaro
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2610.20485
UR - https://arxiv.org/abs/2610.20485
AB - We prove a maximal diameter rigidity theorem for closed 3-dimensional Riemannian manifolds under a spectral lower bound for the Ricci curvature. We show that if 0<γ<2, K>0 and λ_1(−γΔ+Ric)≥ 2K, then the optimal bound diam(M,g)≤π/√K is attained if and only if (M,g) is isometric to the round 3-sphere of constant sectional curvature K.
ER -