Convergence properties of Donaldson's $T$-iterations on the Riemann sphere

Details Convergence properties of Donaldson's $T$-iterations on the Riemann sphere Convergence properties of Donaldson's $T$-iterations on the Riemann sphere

2007-06-28

arxiv.org/abs/0706.4338v2

Mathematics

Differential Geometry

17 pages, 2 figures. The version uses a more natural notion of distance on the space of hermitian metrics, and includes invest

Scientific paper

In a recent paper Donaldson defines three operators on a space of Hermitian metrics on a complex projective manifold: $T, T_{\nu}, T_K.$ Iterations of these operators converge to balanced metrics, and these themselves approximate constant scalar curvature metrics. In this paper we investigate the convergence properties of these iterations by examining the case of the Riemann sphere as well as higher dimensional $\mathbb{CP}^n$.

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