70 citations · 318 across the 22 of their papers we have counts for
6 papers · 1 filter
Buser's inequality on infinite graphs
Shuang Liu
In this paper, we establish Buser type inequalities, i.e., upper bounds for eigenvalues in terms of Cheeger constants. We prove the Buser's inequality for an infinite but locally f…
Li-Yau inequality for unbounded Laplacian on graphs
Chao Gong, Yong Lin, Shuang Liu +1
In this paper, we derive Li-Yau inequality for unbounded Laplacian on complete weighted graphs with the assumption of the curvature-dimension inequality , which can be r…
Global gradient estimate on graph and its applications
Yong Lin, Shuang Liu, Yunyan Yang
Continuing our previous work (arXiv:1509.07981v1), we derive another global gradient estimate for positive functions, particularly for positive solutions to the heat equation on fi…
A gradient estimate for positive functions on graphs
Yong Lin, Shuang Liu, Yunyan Yang
We derive a gradient estimate for positive functions, in particular for positive solutions to the heat equation, on finite or locally finite graphs. Unlike the well known Li-Yau es…
Ultracontractivity and functional inequalities on infinite graphs
Yong Lin, Shuang Liu, Hongye Song
In this paper, we prove the equivalent of ultracontractive bound of heat semigroup or the uniform upper bound of the heat kernel with the Nash inequality, Log-Sobolev inequalities…
Volume doubling, Poincaré inequality and Guassian heat kernel estimate for nonnegative curvature graphs
Paul Horn, Yong Lin, Shuang Liu +1
By studying the heat semigroup, we prove Li-Yau type estimates for bounded and positive solutions of the heat equation on graphs, under the assumption of the curvature-dimension in…