Communications in Analysis and Geometry

Volume 23 (2015)

Number 5

Davies–Gaffney–Grigor’yan Lemma on graphs

Pages: 1031 – 1068

DOI: http://dx.doi.org/10.4310/CAG.2015.v23.n5.a4

Authors

Frank Bauer (Department of Mathematics, Harvard University, Cambridge Massachusetts, U.S.A.)

Bobo Hua (School of Mathematical Sciences, LMNS, and Shanghai Center for Mathematical Sciences, Fudan University, Shanghai, China; and Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany)

Shing-Tung Yau (Department of Mathematics, Harvard University, Cambridge Massachusetts, U.S.A.)

Abstract

We prove a variant of the Davies–Gaffney–Grigor’yan Lemma for the continuous time heat kernel on graphs. We use it together with the Li–Yau inequality, to obtain strong heat kernel estimates for graphs satisfying the exponential curvature dimension inequality.

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