70 citations · 318 across the 22 of their papers we have counts for
4 papers · 1 filter
Equivalent Properties of CD Inequality on Graph
Yong Lin, Shuang Liu
We study some equivalent properties of the curvature-dimension conditions inequality on infinite, but locally finite graph. These equivalences are gradient estimate, Poin…
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…