Perpetual cutoff method and CDE′(K,N) condition on graphs

Yongtao LIU

doi:10.1007/s11464-021-0943-4

Front. Math. China ›› 2021, Vol. 16 ›› Issue (3) : 783 -800. DOI: 10.1007/s11464-021-0943-4

RESEARCH ARTICLE

Perpetual cutoff method and $C D E ′$ (K,N) condition on graphs

Yongtao LIU ¹^,²^,^†

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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 / $C D E ′$ (K,N)')"> $C D E ′$ (K,N)

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Yongtao LIU. Perpetual cutoff method and

C D E ′

(K,N) condition on graphs. Front. Math. China, 2021, 16(3): 783-800 DOI:10.1007/s11464-021-0943-4

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