Please use this identifier to cite or link to this item: http://arks.princeton.edu/ark:/88435/dsp01vq27zq73r
 Title: Smoothing conic Kahler metrics and the conical Kahler-Ricci flow Authors: Shen, Liangming Advisors: Tian, Gang Contributors: Mathematics Department Subjects: Mathematics Issue Date: 2015 Publisher: Princeton, NJ : Princeton University Abstract: In this thesis, we first give two different smoothing methods for conic K¨ahler metrics. One is constructing an approximating sequence of smooth K¨ahler metrics with the same lower Ricci curvature bound with the original conic K¨ahler metric with some lower Ricci curvature bound based on Tian’s approximation method for the conic K¨ahler-Einstein metric. Another one is constructing a smooth approximating sequence of K¨ahler metrics with uniformly bisectional curvature upper bound, based on C. Li and Y. Rubinstein’s bisectional curvature upper bound estimate for a standard conic metric. Then we will use approximation method to construct solutions to the conical K¨ahler-Ricci flow which preserves the conic structure. After $C^{0}$ and $C^{2}$-estimates for potential functions, we finally obtain a $C^{2,\alpha}$-estimate based on Tian’s method in his PKU thesis. URI: http://arks.princeton.edu/ark:/88435/dsp01vq27zq73r Alternate format: The Mudd Manuscript Library retains one bound copy of each dissertation. Search for these copies in the library's main catalog Type of Material: Academic dissertations (Ph.D.) Language: en Appears in Collections: Mathematics