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Relative volume comparison of Ricci flow

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Abstract

In this paper we derive a relative volume comparison of Ricci flow under a certain local curvature condition. It is a refinement of Perelman’s no local collapsing theorem in Perelman (2002).

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Acknowledgements

The first author was supported by National Natural Science Foundation of China (Grant Nos. 11331001 and 11890661). The second author was supported by Beijing Natural Science Foundation (Grant No. Z180004), National Natural Science Foundation of China (Grant No. 11825105) and Ministry of Education of China (Grant No. 161001). The authors thank the referees for pointing out the typos.

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Authors and Affiliations

  1. School of Mathematical Sciences and Beijing International Center for Mathematical Research, Peking University, Beijing, 100871, China

    Gang Tian

  2. School of Mathematical Sciences, Capital Normal University, Beijing, 100048, China

    Zhenlei Zhang

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  1. Gang Tian
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  2. Zhenlei Zhang
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Correspondence to Zhenlei Zhang.

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Tian, G., Zhang, Z. Relative volume comparison of Ricci flow. Sci. China Math. 64, 1937–1950 (2021). https://doi.org/10.1007/s11425-021-1869-5

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  • DOI: https://doi.org/10.1007/s11425-021-1869-5

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