Communications in Analysis and Geometry

Volume 30 (2022)

Number 8

Li–Yau inequality on virtually Abelian groups

Pages: 1833 – 1848



Shuang Liu (Department of Mathematics, Renmin University of China, Beijing, China)

Gabor Lippner (Department of Mathematics, Northeastern University, Boston, Massachusetts, U.S.A.)


We show that Cayley graphs of virtually Abelian groups satisfy a Li–Yau type gradient estimate despite the fact that they do not satisfy any known variant of the curvature-dimension inequality with non-negative curvature.

Received 3 July 2017

Accepted 7 April 2020

Published 13 July 2023