Rigidity properties of the hypercube via Bakry–Émery curvature

被引：0
|
作者：
Shiping Liu
Florentin Münch
Norbert Peyerimhoff
机构：
[1] University of Science and Technology of China,School of Mathematical Sciences
[2] Max-Planck-Institute for Mathematics in the Sciences Leipzig,Department of Mathematical Sciences
[3] Durham University,undefined
来源：
Mathematische Annalen | 2024年 / 388卷
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摘要：
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.
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页码：1225 / 1259
页数：34
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