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Space of Kähler metrics III--On the lower bound of the Calabi energy and geodesic distance

X. X. Chen
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Abstract

In this paper, we first prove a folklore conjecture on a greatest lower bound of the Calabi energy in all Kähler manifold. Similar result in algebriac setting was obtained by S. K. Donaldson. Secondly, we give an upper/lower bound estimate of the K energy in terms of the geodesic distance and the Calabi energy. This is used to prove a theorem on convergence of Kähler metrics in holomorphic coordinates, with uniform bound on the Ricci curvature and the diameter. Thirdly, we set up a framework for the existence of geodesic rays when an asymptotic direction is given. I

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X. X. Chen. 2006-06-09. Space of Kähler metrics III--On the lower bound of the Calabi energy and geodesic distance. https://arxiv.org/abs/math/0606228

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