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A No Shrinking Breather Theorem for Noncompact Harmonic Ricci Flows

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Abstract

In this paper, we construct an ancient solution by using a given shrinking breather and prove a no shrinking breather theorem for noncompact harmonic Ricci flow under the condition that \({\rm{Sic}}: = {\rm{Ric}} - \alpha \nabla \phi \otimes \nabla \phi \) is bounded from below.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Wuhan University, Wuhan, 430072, P. R. China

    Jia Rui Chen & Qun Chen

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  1. Jia Rui Chen
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  2. Qun Chen
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Correspondence to Qun Chen.

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Conflict of Interest The authors declare no conflict of interest.

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Partially supported by NSFC (Grant No. 11971358)

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Chen, J.R., Chen, Q. A No Shrinking Breather Theorem for Noncompact Harmonic Ricci Flows. Acta. Math. Sin.-English Ser. 39, 1939–1950 (2023). https://doi.org/10.1007/s10114-023-2302-8

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  • DOI: https://doi.org/10.1007/s10114-023-2302-8

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