Smoothing conic Kähler metrics with uniformly upper bisectional curvature bound

Abstract

Based on C. Li and Y. Rubinstein's upper bisectional curvature bound estimate for the conic Kähler metric, we can construct a smoothing sequence for the conic metric with uniformly upper bisectional curvature bound. For the conic metric along a simple normal crossing divisor with triple or higher multiple points we may need to choose a new background Kähler metric in the same cohomology class of the original background metric. This setting will be helpful to the study of conical Kähler-Einstein metrics and conical Kähler-Ricci flow.

This paper has been withdrawn by the author due to a crucial sign error in equation (4.3)

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• $C^{2,\alpha }$-estimate for conical Kähler-Ricci flow