Abstract
In this note, we extend a comparison theorem of minimal Green functions in Munteanu and Wang (https://arxiv.org/abs/2105.12103) to harmonic functions on complete non-compact three-dimensional manifolds with compact connected boundary. This yields an upper bound on the integral related to scalar curvature on complete, non-parabolic three-dimensional manifolds.
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Acknowledgements
The author would like to express his deep gratitude to his advisor Prof. Jiaping Wang for his constant support, guidance, and encouragement. The author is indebted to Prof. Hanlong Fang, Pak-Yeung Chan, Wenshuai Jiang and Zhichao Wang for their discussions and suggestions over the past years. Finally, the author would like to thank the reviewer for his careful reading and suggestions on English writing, which makes this work more readable.
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Zhu, B. Comparison Theorem and Integral of Scalar Curvature on Three Manifolds. J Geom Anal 32, 197 (2022). https://doi.org/10.1007/s12220-022-00934-y
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DOI: https://doi.org/10.1007/s12220-022-00934-y