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arXiv · 0803.1249

Bergman approximations of harmonic maps into the space of Kahler metrics on toric varieties

Yanir A. Rubinstein·Steve Zelditch
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Abstract

We generalize the results of Song-Zelditch on geodesics in spaces of Kahler metrics on toric varieties to harmonic maps of any compact Riemannian manifold with boundary into the space of Kahler metrics on a toric variety. We show that the harmonic map equation can always be solved and that such maps may be approximated in the C^2 topology by harmonic maps into the spaces of Bergman metrics. In particular, WZW maps, or equivalently solutions of a homogeneous Monge-Ampere equation on the product of the manifold with a Riemann surface with S^1 boundary admit such approximations. We also show that the Eells-Sampson flow on the space of Kahler potentials is transformed to the usual heat flow on the space of symplectic potentials under the Legendre transform.

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Yanir A. Rubinstein, Steve Zelditch. 2008-03-08. Bergman approximations of harmonic maps into the space of Kahler metrics on toric varieties. https://arxiv.org/abs/0803.1249

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