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doi:10.1007/s11464-021-0943-4

Front. Math. China

2021, Vol. 16

Issue (3) : 783-800 https://doi.org/10.1007/s11464-021-0943-4

RESEARCH ARTICLE

Perpetual cutoff method and

C D E ′

(K,N) condition on graphs

Yongtao LIU^1,²(

)

¹. School of Mathematical Sciences, Capital Normal University, Beijing 100048, China
². School of Mathematics and Statistics, Ningxia University, Yinchuan 750021, China

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Abstract

By using the perpetual cutoff method, we prove two discrete versions of gradient estimates for bounded Laplacian on locally finite graphs with exception sets under the condition of $C D E ′$ (K,N). This generalizes a main result of F. Münch who considers the case of CD(K, $∞$ ) curvature. Hence, we answer a question raised by Münch. For that purpose, we characterize some basic properties of radical form of the perpetual cutoff semigroup and give a weak commutation relation between bounded Laplacian $Δ$ and perpetual cutoff semigroup $P t W$ in our setting.

Keywords Locally finite graphs perpetual cutoff method gradient estimates CDE′(K,N)')" href="#">

C D E ′

(K,N)

Corresponding Author(s): Yongtao LIU

Issue Date: 14 July 2021

Cite this article:

Yongtao LIU. Perpetual cutoff method and

C D E ′

(K,N) condition on graphs[J]. Front. Math. China, 2021, 16(3): 783-800.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-021-0943-4
https://academic.hep.com.cn/fmc/EN/Y2021/V16/I3/783

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