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Entropy and Heat Kernel on Generalized Ricci Flow

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Abstract

We introduce analogous geometric quantities and prove some geometric and analytic bounds in [1] to generalized Ricci flow.

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References

  1. Bamler, R.H.: Entropy and heat kernel bounds on a Ricci flow background (2020). arXiv:2008.07093

  2. Bamler, R.H.: Compactness theory of the space of Super Ricci flows (2020). arXiv:2008.09298

  3. Bamler, R.H.: Structure theory of non-collapsed limits of Ricci flows (2020). arXiv:2009.03243

  4. Chow, B., Chu, S.-C., Glickenstein, D., Guenther, C., Isenberg, J., Ivey, T., Knopf, D., Lu, P., Luo, F., Ni, L.: The Ricci flow: techniques and applications. Part III. Geometric-analytic aspects, Mathematical Surveys and Monographs, Vol. 163, American Mathematical Society, Providence, RI (2010). https://doi.org/10.1090/surv/163

  5. Gauduchon, P.: Le théorème de l’excentricité nulle, C. R. Acad. Sci. Paris Sér. A-B 285, A387–A390 (1977)

    MathSciNet  Google Scholar 

  6. Garcia-Fernandez, M., Streets, J.: Generalized Ricci Flow, University Lecture Series, vol. 76. American Mathematical Society, Providence, RI (2021). https://doi.org/10.1090/ulect/076

    Book  Google Scholar 

  7. Guenther, C.M.: The fundamental solution on manifolds with time-dependent metrics. J. Geom. Anal. 12, 425–436 (2002). https://doi.org/10.1007/BF02922048

    Article  MathSciNet  Google Scholar 

  8. Hein, H.-J., Naber, A.: New logarithmic Sobolev inequalities and an \(\epsilon \)-regularity theorem for the Ricci flow. Comm. Pure Appl. Math. 67, 1543–1561 (2014). https://doi.org/10.1002/cpa.21474

    Article  MathSciNet  Google Scholar 

  9. Streets, J., Tian, G.: A parabolic flow of pluriclosed metrics. Int. Math. Res. Not. IMRN (2010). https://doi.org/10.1093/imrn/rnp237

    Article  MathSciNet  Google Scholar 

  10. Streets, J., Tian, G.: Regularity results for pluriclosed flow. Geom. Topol. 17, 2389–2429 (2013). https://doi.org/10.2140/gt.2013.17.2389

    Article  MathSciNet  Google Scholar 

  11. Streets, J.: Ricci-Yang-Mills flow on surfaces and pluriclosed flow on elliptic fibrations. Adv. Math. 394, Paper No. 108127, 31 (2022). https://doi.org/10.1016/j.aim.2021.108127

  12. Streets, J.: Scalar curvature, entropy, and generalized Ricci flow (2022). arXiv:2207.13197

  13. Ye, Y.: Derivative estimates of pluriclosed flow (2023). arXiv:2308.14600

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Acknowledgements

I am grateful to my advisor Professor Gang Tian for his helpful guidance. I thank Yanan Ye and Shengxuan Zhou for inspiring discussions.

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  1. SMS, Peking University, Beijing, 100871, China

    Xilun Li

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  1. Xilun Li
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Correspondence to Xilun Li.

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Li, X. Entropy and Heat Kernel on Generalized Ricci Flow. J Geom Anal 34, 42 (2024). https://doi.org/10.1007/s12220-023-01488-3

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  • DOI: https://doi.org/10.1007/s12220-023-01488-3

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