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The \(C^{2,\alpha }\)-estimate for conical Kähler–Ricci flow

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Abstract

In this note, we establish a parabolic version of Tian’s \(C^{2,\alpha }\)-estimate for conical complex Monge–Ampere equations (Tian in Chin Ann Math Ser B 38(2):687–694, 2017), which includes conical Kähler–Einstein metrics. Our estimate will complete the proof of the existence of unnormalized conical Kähler–Ricci flow in Shen (J Reine Angew Math, [28]).

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Acknowledgements

First the author wants to thank his Ph.D thesis advisor Professor Gang Tian for a lot of discussions and encouragement. And he also wants to thank Chi Li, Yanir Rubinstein and Zhenlei Zhang for many useful conversations. And he also thanks CSC for partial financial support during his Ph.D career.

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  1. Department of Mathematics, The University of British Columbia, Vancouver, BC, V6T 1Z4, Canada

    Liangming Shen

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  1. Liangming Shen
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Correspondence to Liangming Shen.

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Communicated by A.Chang.

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Shen, L. The \(C^{2,\alpha }\)-estimate for conical Kähler–Ricci flow. Calc. Var. 57, 33 (2018). https://doi.org/10.1007/s00526-018-1308-z

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