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Convergence of Bergman geodesics on CP^1

The space of positively curved hermitian metrics on a positive holomorphic line bundle over a compact complex manifold is an infinite-dimensional symmetric space. It is shown by Phong and Sturm that geodesics in this space can be uniformly approximated by geodesics in the finite dimensional spaces of Bergman metrics. We prove a stronger C^2-approximation in the special case of toric (i.e. S^1-invariant) metrics on CP^1.

preprint2007arXivOpen access
Jian SongSteve Zelditch
math.DG
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Jian SongSteve Zelditch

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