The Monge-Amp\`ere operator and geodesics in the space of K\"ahler potentials
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🧮 math.DG
math.CV
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ahlergeodesicspotentialsspaceadaptedapproximatedapproximationbedford-taylor
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It is shown that geodesics in the space of K\"ahler potentials can be uniformly approximated by geodesics in the spaces of Bergman metrics. Two important tools in the proof are the Tian-Yau-Zelditch approximation theorem for K\"ahler potentials and the pluripotential theory of Bedford-Taylor, suitably adapted to K\"ahler manifolds.
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