Generalized Kähler–Einstein Metrics andEnergy Functionals
Canadian journal of mathematics, Tome 66 (2014) no. 6, pp. 1413-1435
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In this paper, we consider a generalized Kähler–Einstein equation on a Kähler manifold $M$ . Using the twisted $\mathcal{K}$ –energy introduced by Song and Tian, we show that the existence of generalized Kähler–Einstein metrics with semi–positive twisting (1, 1)–form $\theta$ is also closely related to the properness of the twisted $\mathcal{K}$ -energy functional. Under the condition that the twisting form $\theta$ 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.
Mots-clés :
53C55, 32W20, complex Monge–Ampère equation, energy functional, generalized Kähler–Einstein metric, Moser–Trudinger type inequality
Zhang, Xi; Zhang, Xiangwen. Generalized Kähler–Einstein Metrics andEnergy Functionals. Canadian journal of mathematics, Tome 66 (2014) no. 6, pp. 1413-1435. doi: 10.4153/CJM-2013-034-3
@article{10_4153_CJM_2013_034_3,
author = {Zhang, Xi and Zhang, Xiangwen},
title = {Generalized {K\"ahler{\textendash}Einstein} {Metrics} {andEnergy} {Functionals}},
journal = {Canadian journal of mathematics},
pages = {1413--1435},
year = {2014},
volume = {66},
number = {6},
doi = {10.4153/CJM-2013-034-3},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2013-034-3/}
}
TY - JOUR AU - Zhang, Xi AU - Zhang, Xiangwen TI - Generalized Kähler–Einstein Metrics andEnergy Functionals JO - Canadian journal of mathematics PY - 2014 SP - 1413 EP - 1435 VL - 66 IS - 6 UR - http://geodesic.mathdoc.fr/articles/10.4153/CJM-2013-034-3/ DO - 10.4153/CJM-2013-034-3 ID - 10_4153_CJM_2013_034_3 ER -
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