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Generalized Matsushima's theorem and Kahler-Einstein cone metrics
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Li, Long and Zheng, Kai (2018) Generalized Matsushima's theorem and Kahler-Einstein cone metrics. Calculus of Variations and Partial Differential Equations, 57 . 31. doi:10.1007/s00526-018-1313-2 ISSN 0944-2669.
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Official URL: http://doi.org/10.1007/s00526-018-1313-2
Abstract
In this paper, we first prove a generalized Matsushima’s
theorem, i.e. the automorphism group is reductive on a Fano
manifold admitting K¨ahler-Einstein metrics with cone singularities
along a smooth divisor. Note that the divisor in our paper is
not necessarily proportional to the anti-canonical class. We then
give an alternative proof of uniqueness of K¨ahler-Einstein cone
metrics by combining the reductivity of the automorphism group
with the continuity method, the approximation trick and the bifurcation technique. Moreover, our method provides an existence
theorem of K¨ahler-Einstein cone metrics with respect to conic Ding
functional.
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): | Geometry, Differential, Complex manifolds | |||||||||
Journal or Publication Title: | Calculus of Variations and Partial Differential Equations | |||||||||
Publisher: | Springer | |||||||||
ISSN: | 0944-2669 | |||||||||
Official Date: | April 2018 | |||||||||
Dates: |
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Volume: | 57 | |||||||||
Article Number: | 31 | |||||||||
DOI: | 10.1007/s00526-018-1313-2 | |||||||||
Status: | Peer Reviewed | |||||||||
Publication Status: | Published | |||||||||
Access rights to Published version: | Restricted or Subscription Access | |||||||||
Date of first compliant deposit: | 8 February 2018 | |||||||||
RIOXX Funder/Project Grant: |
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