Abstract
Motivated and inspired by the recent work of Colding (Acta Math 209(2):229–263, 2012) and Colding and Minicozzi (Calc Var Partial Differ Equ 49(3–4):1045–1059, 2014) we derive several families of monotonicity formulas for manifolds with nonnegative Bakry–Emery Ricci curvature, extending the formulas in Colding (2012) and Colding and Minicozzi (2014).
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Acknowledgments
The authors would like to thank the referee for helpful suggestions, Toby Colding for his interest and encouragement, and Toby Colding and Bill Minicozzi for answering our questions on their work. This work was done while the first and third authors were visiting UCSB. They would like to thank UCSB for hospitality during their stay. The work was partially supported by NSFC Grant No. 11171259 and by NSF Grant # DMS-1105536.
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Communicated by Jiaping Wang.
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Song, B., Wei, G. & Wu, G. Monotonicity Formulas for the Bakry–Emery Ricci Curvature. J Geom Anal 25, 2716–2735 (2015). https://doi.org/10.1007/s12220-014-9533-y
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DOI: https://doi.org/10.1007/s12220-014-9533-y