Perpetual cutoff method and (K,N) condition on graphs |
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Authors: | Yongtao LIU |
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Institution: | 1. School of Mathematical Sciences, Capital Normal University, Beijing 100048, China2. 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 (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 and perpetual cutoff semigroup in our setting. |
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Keywords: | Locally finite graphs perpetual cutoff method gradient estimates org/1998/Math/MathML" altimg="c:\heptemp\HML634036 png" baseline="-0 CDE′(K" target="_blank">5" display="inline">CDE′(K N) |
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