Rigidity properties of the hypercube via Bakry–Émery curvature

Liu, Shiping; Münch, Florentin; Peyerimhoff, Norbert

doi:10.1007/s00208-022-02537-y

Rigidity properties of the hypercube via Bakry–Émery curvature

Liu, Shiping; Münch, Florentin; Peyerimhoff, Norbert

Authors

Shiping Liu

Florentin Münch

Professor Norbert Peyerimhoff norbert.peyerimhoff@durham.ac.uk
Professor

Abstract

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.

Citation

Liu, S., Münch, F., & Peyerimhoff, N. (2024). Rigidity properties of the hypercube via Bakry–Émery curvature. Mathematische Annalen, 388(2), 1225-1259. https://doi.org/10.1007/s00208-022-02537-y

Journal Article Type	Article
Acceptance Date	Dec 5, 2022
Online Publication Date	Dec 26, 2022
Publication Date	2024-02
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
Volume	388
Issue	2
Pages	1225-1259
DOI	https://doi.org/10.1007/s00208-022-02537-y
Public URL	https://durham-repository.worktribe.com/output/1183040

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