TY - JOUR
T1 - Li-Yau inequality for unbounded Laplacian on graphs
AU - Gong, Chao
AU - Lin, Yong
AU - Liu, Shuang
AU - Yau, Shing Tung
N1 - Publisher Copyright:
© 2019 Elsevier Inc.
PY - 2019/12/1
Y1 - 2019/12/1
N2 - In this paper, we derive Li-Yau inequality for unbounded Laplacian on complete weighted graphs with the assumption of the curvature dimension inequality CDE′(n,K), which can be regarded as a notion of curvature on graphs. Furthermore, we obtain some applications of Li-Yau inequality, including Harnack inequality, heat kernel bounds and Cheng's eigenvalue estimate. These are the first kind of results in this direction for unbounded Laplacian on graphs.
AB - In this paper, we derive Li-Yau inequality for unbounded Laplacian on complete weighted graphs with the assumption of the curvature dimension inequality CDE′(n,K), which can be regarded as a notion of curvature on graphs. Furthermore, we obtain some applications of Li-Yau inequality, including Harnack inequality, heat kernel bounds and Cheng's eigenvalue estimate. These are the first kind of results in this direction for unbounded Laplacian on graphs.
KW - Cheng's eigenvalue estimate
KW - Heat kernel
KW - Li-Yau inequality on graphs
KW - Unbounded Laplacians
UR - http://www.scopus.com/inward/record.url?scp=85072822887&partnerID=8YFLogxK
U2 - 10.1016/j.aim.2019.106822
DO - 10.1016/j.aim.2019.106822
M3 - Article
AN - SCOPUS:85072822887
SN - 0001-8708
VL - 357
JO - Advances in Mathematics
JF - Advances in Mathematics
M1 - 106822
ER -