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

Morgan Sherman

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

Differential Geometry 2008-08-25 v2 Numerical Analysis

Authors: Morgan Sherman

Abstract

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 $\mathbb{CP}^n$ .

Keywords

Donaldson's T-iterations Hermitian metrics balanced metrics constant scalar curvature Riemann sphere complex projective manifold

Cite

@article{arxiv.0706.4338,
  title  = {Convergence properties of Donaldson's $T$-iterations on the Riemann sphere},
  author = {Morgan Sherman},
  journal= {arXiv preprint arXiv:0706.4338},
  year   = {2008}
}

Comments

17 pages, 2 figures. The version uses a more natural notion of distance on the space of hermitian metrics, and includes investigations in the case of $\mathbb{CP}^n$

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

Abstract

Keywords

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