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Rigidity in sharp eigenvalue estimates for differential forms
Abstract
For 1≤ p≤ n/2, we derive sharp eigenvalue estimates for the Hodge Laplacian on differential p-forms under the curvature condition introduced by Petersen and Wink, and study their equality cases. Equality recovers the stronger curvature operator lower bound and, in the closed case, leaves only round or Sasakian metrics on the universal cover. For manifolds with boundary, weak p-convexity of the boundary makes the unit hemisphere the only equality case for the absolute boundary problem.
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BibTeX
@misc{chow2026rigidity,
title = {{Rigidity in sharp eigenvalue estimates for differential forms}},
author = {Tsz-Kiu Aaron Chow and James Koh and Sen Yuk Wu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.41297},
eprint = {2610.41297},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.41297},
}
RIS
TY - UNPB
TI - Rigidity in sharp eigenvalue estimates for differential forms
AU - Tsz-Kiu Aaron Chow
AU - James Koh
AU - Sen Yuk Wu
PY - 2026
DA - 2026/10/30
PB - arXiv
DO - 10.48550/arxiv.2610.41297
UR - https://arxiv.org/abs/2610.41297
AB - For 1≤ p≤ n/2, we derive sharp eigenvalue estimates for the Hodge Laplacian on differential p-forms under the curvature condition introduced by Petersen and Wink, and study their equality cases. Equality recovers the stronger curvature operator lower bound and, in the closed case, leaves only round or Sasakian metrics on the universal cover. For manifolds with boundary, weak p-convexity of the boundary makes the unit hemisphere the only equality case for the absolute boundary problem.
ER -