标题： 柏格曼逼近调和映射到凯勒度量的空间上环面簇 显示英文标题

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

摘要： 我们将Song-Zelditch关于环簇上Kähler度量空间中测地线的结果推广到任意具有边界的紧致Riemann流形上的调和映射进入环簇的Kähler度量空间的情形。我们证明了调和映射方程总是可解的，并且这类映射可以用C^2拓扑逼近到Bergman度量空间上的调和映射。特别是，WZW映射（或等价地，满足齐次Monge-Ampère方程的解）在流形与具有S^1边界的黎曼曲面乘积上的解可以接受这种逼近。我们还证明了Kähler位势空间上的Eells-Sampson流在Legendre变换下变为辛位势空间上的通常热流。 显示英文摘要

摘要： 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.