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Chiung-Ju Liu 
2010-03-23 
10:20 - 11:20 
308 , Mathematics Research Center Building (ori. New Math. Bldg.)

The asymptotic expansion of Tian-Yau-Zelditch plays an important role in recent complex differential geometry. Donaldson shows that metric of a constant scalar curvature on a polarized manifold is the limit of balanced matric with using the expansion of Zelditch. We consider a more generalized case by twisting the polarized line bundle with a holomorphic vector bundle. By using Tian's peak sections and a variation of K-coordinates and K-frames, we are able to show the original expansion. If the metrics are analytic, we are able to show the convergence of the expansion.