Kähler non-collapsing,eigenvalues and the Calabi flow |
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| Authors: | Haozhao Li Kai Zheng |
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| Affiliation: | 1. Department of Mathematics, University of Science and Technology of China, Hefei, 230026, Anhui, China;2. Wu Wen-Tsun Key Laboratory of Mathematics, USTC, Chinese Academy of Sciences, Hefei, 230026, Anhui, China;3. Institut für Differentialgeometrie, Leibniz Universität Hannover, Welfengarten 1, 30167 Hannover, Germany |
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| Abstract: | We first prove a new compactness theorem of Kähler metrics, which confirms a prediction in [17]. Then we establish several eigenvalue estimates along the Calabi flow. Combining the compactness theorem and these eigenvalue estimates, we generalize the method developed for the Kähler–Ricci flow in [22] to obtain several new small energy theorems of the Calabi flow. |
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| Keywords: | primary, 53C44 secondary, 32Q15, 32Q26, 58E11 |
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