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arXiv:1309.4304 [math.DG]AbstractReferencesReviewsResources

Kähler non-collapsing, eigenvalues and the Calabi flow

Haozhao Li, Kai Zheng

Published 2013-09-17, updated 2014-06-28Version 2

We first proved a compactness theorem of the K\"ahler metrics, which confirms a prediction of Chen. Then we prove several eigenvalue estimates along the Calabi flow. Combining the compactness theorem and these eigenvalue estimates, we generalize the method developed by Chen-Li-Wang to prove the small energy theorems of the Calabi flow.

Comments: 33 pages, final version, to appear in Journal of Functional Analysis
Categories: math.DG
Subjects: 53C44
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