Generalized Kähler–Einstein Metrics andEnergy Functionals

Zhang, Xi ; Zhang, Xiangwen

Canadian journal of mathematics, Tome 66 (2014) no. 6, pp. 1413-1435

Résumé

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.

Détail

DOI : 10.4153/CJM-2013-034-3

Mots-clés : 53C55, 32W20, complex Monge–Ampère equation, energy functional, generalized Kähler–Einstein metric, Moser–Trudinger type inequality

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