Harnack inequalities for graphs with non-negative Ricci curvature
By Fan Chung, Yong Lin, Shing-Tung Yau. 2012
72 citations recorded by the source corpus.
We establish a Harnack inequality for finite connected graphs with non-negative Ricci curvature. As a consequence, we derive an eigenvalue lower bound, extending previous results for Ricci flat graphs.
Subfields: Applied Mathematics, Astronomy and Astrophysics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/c9f8dc7e9fc532a67a78cc7d9cec23047d6526ad
How researchers see this paper
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In Applied Mathematics
- Shiping Liu
- Norbert Peyerimhoff
- Gady Kozma
- Florentin Münch
- David Cushing
- Prasad Tetali
- Peter Ralli
- Bo'az Klartag
In Astronomy and Astrophysics
- Norbert Peyerimhoff
- Shiping Liu
- Florentin Münch
- David Cushing
- Prasad Tetali
- Gady Kozma
- Peter Ralli
- Bo'az Klartag
In Geometry and Topology
- Norbert Peyerimhoff
- Shiping Liu
- Florentin Münch
- David Cushing
- Prasad Tetali
- Gady Kozma
- Peter Ralli
- Bo'az Klartag
Citations in the corpus
- Discrete Curvature and Abelian Groups (2015, background): “We thank the referee for bringing a lot of relevant literature to our attention, especially [11, 12,27,29].”
- Li–Yau inequality on finite graphs via non-linear curvature dimension conditions (2014, background): “On graphs, it has been studied in [5, 6, 10, 13, 15, 16].”
- Bakry–Émery Curvature Functions on Graphs (2016, background): “This follows from two estimates for the eigenvalue λ1(∆) of the Laplacian ∆ of G: A Lichnerowicz type estimate (see [10, 21]) tells λ1(∆) ≥ KG(∞); Friedman, Murty, and Tillich [14] prove that there exists an absolute constant C such that for any abelian Cayley graph, λ1(∆) ≤ CdN− 4 d .”