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Regularity scales and convergence of the Calabi flow
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Li, Haozhao, Wang, Bing and Zheng, Kai (2018) Regularity scales and convergence of the Calabi flow. The Journal of Geometric Analysis, 28 (3). pp. 2050-2101. doi:10.1007/s12220-017-9896-y ISSN 1050-6926.
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Official URL: https://doi.org/10.1007/s12220-017-9896-y
Abstract
We define regularity scales to study the behavior of the Calabi flow. Based on estimates of the regularity scales, we obtain convergence theorems of the Calabi flow on extremal Kähler surfaces, under the assumption of global existence of the Calabi flow solutions. Our results partially confirm Donaldson’s conjectural picture for the Calabi flow in complex dimension 2. Similar results hold in high dimension with an extra assumption that the scalar curvature is uniformly bounded.
Item Type: | Journal Article | ||||||||||||
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Subjects: | Q Science > QA Mathematics | ||||||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||||||
Library of Congress Subject Headings (LCSH): | Calabi-Yau manifolds, Kählerian manifolds | ||||||||||||
Journal or Publication Title: | The Journal of Geometric Analysis | ||||||||||||
Publisher: | Springer New York LLC | ||||||||||||
ISSN: | 1050-6926 | ||||||||||||
Official Date: | July 2018 | ||||||||||||
Dates: |
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Volume: | 28 | ||||||||||||
Number: | 3 | ||||||||||||
Number of Pages: | 52 | ||||||||||||
Page Range: | pp. 2050-2101 | ||||||||||||
DOI: | 10.1007/s12220-017-9896-y | ||||||||||||
Status: | Peer Reviewed | ||||||||||||
Publication Status: | Published | ||||||||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||||||||
Date of first compliant deposit: | 20 November 2017 | ||||||||||||
Date of first compliant Open Access: | 11 July 2018 | ||||||||||||
RIOXX Funder/Project Grant: |
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