Generalized Kähler–Einstein Metrics and
Energy Functionals
2014 ◽
Vol 66
(6)
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pp. 1413-1435
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Keyword(s):
Abstract.In this paper, we consider a generalized Kähler–Einstein equation on a Kähler manifold M. Using the twisted 𝒦–energy introduced by Song and Tian, we show that the existence of generalized Kähler–Einstein metrics with semi–positive twisting (1, 1)–form θ is also closely related to the properness of the twisted 𝒦-energy functional. Under the condition that the twisting form θ is strictly positive at a point or M admits no nontrivial Hamiltonian holomorphic vector field, we prove that the existence of generalized Kähler–Einstein metric implies a Moser–Trudinger type inequality.
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2021 ◽
Vol 0
(0)
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Keyword(s):
2013 ◽
Vol 24
(10)
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pp. 1350077
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2013 ◽
Vol 24
(05)
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pp. 1350035
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2004 ◽
Vol 06
(02)
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pp. 301-313
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1972 ◽
Vol 46
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pp. 161-173
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