Numerical Algorithms for Finding Balanced Metrics on Vector Bundles

Details Numerical Algorithms for Finding Balanced Metrics on Vector Bundles Numerical Algorithms for Finding Balanced Metrics on Vector Bundles

2008-04-24

arxiv.org/abs/0804.4005v2

Mathematics

Differential Geometry

Scientific paper

In \cite{D3}, Donaldson defines a dynamical system on the space of Fubini-Study metrics on a polarized compact K\"ahler manifold. Sano proved that if there exists a balanced metric for the polarization, then this dynamical system always converges to the balanced metric (\cite{S}). In \cite{DKLR}, Douglas, et. al., conjecture that the same holds in the case of vector bundles. In this paper, we give an affirmative answer to their conjecture.

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