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Rigidity properties of the hypercube via Bakry–Émery curvature

Liu, Shiping; Münch, Florentin; Peyerimhoff, Norbert

Rigidity properties of the hypercube via Bakry–Émery curvature Thumbnail


Shiping Liu

Florentin Münch


We give rigidity results for the discrete Bonnet–Myers diameter bound and the Lichnerowicz eigenvalue estimate. Both inequalities are sharp if and only if the underlying graph is a hypercube. The proofs use well-known semigroup methods as well as new direct methods which translate curvature to combinatorial properties. Our results can be seen as first known discrete analogues of Cheng’s and Obata’s rigidity theorems.


Liu, S., Münch, F., & Peyerimhoff, N. (in press). Rigidity properties of the hypercube via Bakry–Émery curvature. Mathematische Annalen,

Journal Article Type Article
Acceptance Date Dec 5, 2022
Online Publication Date Dec 26, 2022
Deposit Date Jan 23, 2023
Publicly Available Date Jan 23, 2023
Journal Mathematische Annalen
Print ISSN 0025-5831
Electronic ISSN 1432-1807
Publisher Springer
Peer Reviewed Peer Reviewed


Published Journal Article (Online first) (869 Kb)

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Online first This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit

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