Space of Kähler metrics III – On the lower bound of the Calabi energy and geodesic distance
By Xiuxiong Chen. 2006
113 citations recorded by the source corpus.
In this paper, we first prove a folklore conjecture on a greatest lower bound of the Calabi energy in all K\"ahler 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 K\"ahler 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
Subfields: Applied Mathematics, Astronomy and Astrophysics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/0ebb6b74f3f75b677b3f6d9e95362a490590287c
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Applied Mathematics
In Astronomy and Astrophysics
In Geometry and Topology
Citations in the corpus
- Long time existence of Minimizing Movement solutions of Calabi flow (2012, methodology): “In preparing our application of Mayer’s theorem a crucial role is played throughout by the theory of geodesics in H developed in the work of Chen, [6], [7], Calabi-Chen [4], and Chen-Tian [11].”
- On Einstein, Hermitian 4-Manifolds (2010, background): “uations are equivalent to requiring that ∇1,0s be a holomorphic vector field. In fact, every extremal Ka¨hler metric turns out to be an absolute minimizer for the Calabi problem, and the proof of this [7] moreover implies that any Ka¨hler metric g with Ka¨hler class [ω] = Ω satisfies the sharp estimat”