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Energy Properness and Sasakian-Einstein Metrics

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Abstract

In this paper, we show that the existence of Sasakian-Einstein metrics is closely related to the properness of corresponding energy functionals. Under the condition of admitting no nontrivial Hamiltonian holomorphic vector field, we prove that the existence of Sasakian-Einstein metric implies a Moser-Trudinger type inequality. At the end of this paper, we also obtain a Miyaoka-Yau type inequality in Sasakian geometry.

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Authors and Affiliations

  1. Department of Mathematics, Zhejiang University, Hangzhou, 310027, P.R. China

    Xi Zhang

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  1. Xi Zhang
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Correspondence to Xi Zhang.

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Communicated by P.T. Chruściel

The author was supported in part by NSF in China, No.10831008 and No.11071212.

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Zhang, X. Energy Properness and Sasakian-Einstein Metrics. Commun. Math. Phys. 306, 229–260 (2011). https://doi.org/10.1007/s00220-011-1292-z

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  • DOI: https://doi.org/10.1007/s00220-011-1292-z

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