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Analysis Aspects of Ricci Flow on Conical Surfaces

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Abstract

In this paper, we establish a framework for the analysis of linear parabolic equations on conical surfaces and use them to study the conical Ricci flow. In particular, we prove the long time existence of the conical Ricci flow for general cone angle and show that this solution has the optimal regularity, namely, the time derivatives of the conformal factor are bounded and for each fixed time, the conformal factor has an explicit asymptotic expansion near the cone points.

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Acknowledgements

A major part of this paper was finished during the author’s visit in Warwick University in 2015. He would like to thank the Mathematics Institute for the wonderful working environment and Professor Topping for making it available to him.

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Authors and Affiliations

  1. School of Mathematical Sciences, University of Science and Technology of China, Hefei, 230026, P. R. China

    Hao Yin

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  1. Hao Yin
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Correspondence to Hao Yin.

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Supported by NSFC (Grant Nos. 11471300, 11971451 and 2020YFA0713102)

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Yin, H. Analysis Aspects of Ricci Flow on Conical Surfaces. Acta. Math. Sin.-English Ser. 38, 807–857 (2022). https://doi.org/10.1007/s10114-022-0131-9

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  • DOI: https://doi.org/10.1007/s10114-022-0131-9

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