Deformation of conic negative Kähler-Einstein manifolds

Abstract

In this note, we investigate the behavior of a smooth flat family of n-dimensional conic negative Kähler-Einstein manifolds. By H. Guenancia’s argument, a cusp negative Kähler-Einstein metric is the limit of conic negative Kähler-Einstein metric when the cone angle tends to 0. Furthermore, it establishes the behavior of a smooth flat family of n-dimensional cusp negative Kähler-Einstein manifolds.

Key words： Conic Kähler-Einstein metric,; C_{\mathrm{l}\mathrm{o}\mathrm{c}}^{\infty }convergence

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