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On the Dirichlet problem for a class of singular complex Monge—Ampère equations

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Abstract

We study the Dirichlet problem of the n-dimensional complex Monge—Ampère equation det(u ij̅ ) = F/|z|2α, where 0 < α < n. This equation comes from La Nave—Tian’s continuity approach to the Analytic Minimal Model Program.

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Acknowledgements

This work is part of the first author’s thesis at Nanjing University. He would like to thank his advisor Professor Gang Tian for suggesting this problem and for his encouragement. The authors thank Dr. Xumin Jiang for bringing [6] to their sight and thank Professor Zhenlei Zhang for helpful discussions concerning the continuity approach to analytic MMP. They also thank Professor Xinan Ma for his interest in this work.

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Authors and Affiliations

  1. Department of Mathematics, Nanjing University, Nanjing, 210093, P. R. China

    Ke Feng, Ya Long Shi & Yi Yan Xu

Authors
  1. Ke Feng
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  2. Ya Long Shi
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  3. Yi Yan Xu
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Corresponding author

Correspondence to Ya Long Shi.

Additional information

The second author is supported by NSFC (Grant No. 11331001); the third author is supported by NSFC (Grant No. 11501285)

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Feng, K., Shi, Y.L. & Xu, Y.Y. On the Dirichlet problem for a class of singular complex Monge—Ampère equations. Acta. Math. Sin.-English Ser. 34, 209–220 (2018). https://doi.org/10.1007/s10114-017-7148-5

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  • DOI: https://doi.org/10.1007/s10114-017-7148-5

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