In this paper we prove the existence and uniqueness of the form-type equation on Kähler manifolds of nonnegative orthogonal bisectional curvature.
This is a preview of subscription content,to check access.
Access this article
Błocki, Z.: On uniform estimate in Calabi–Yau Theorem. Sci. China Ser. A Math. 48, 244–247 (2005)
Fu, J.-X., Wang, Z., Wu, D.: Form-type Calabi–Yau equations. Math. Res. Lett. 17, 887–903 (2010)
Gilbarg, D., Trudinger, N.: Elliptic Partial Differential Equations of Second order, Springer, Berlin, Paperback edition, (2001)
Gu, H.-L., Zhang, Z.-H.: An extension of Mok’s Theorem on the generalized Frankel conjecture. Sci. China Math. 53, 1253–1264 (2010)
Guan, B., Li, Q.: Complex Monge–Ampère equations and totally geodesic manifolds. Adv. Math. 225, 1185–1223 (2010)
Han, Q., Lin, F.: Elliptic partial differential equations. In: Courant Lecture Notes in Mathematics, vol. 1, AMS Press, Brooklyn (2000)
Mok, N.: The Uniformization theorem for compact Kähler manifolds of nonnegative holomorphic bisectional curvature. J. Differ. Geom. 27, 179–214 (1988)
Siu, Y.-T., Yau, S.-T.: Complex Kähler manifolds of positive bisectional curvature. Invent. Math. 59, 189–204 (1980)
Tosatti, V., Weinkove, B.: The complex Monge–Ampère equation on compact Hermitian manifolds. J. Am. Math. Soc. 23, 1187–1195 (2010)
Yau, S.-T.: On the Ricci curvature of a compact Kähler manifold and the complex Monge–Ampère equation, I. Commun. Pure Appl. Math. 31, 339–411 (1978)
The authors would like to thank Professor S.-T. Yau for helpful discussion. Part of the work was done while the third named author was visiting Fudan University, and he would like to thank their warm hospitality. Fu is supported in part by NSFC grants 10831008 and 11025103.
Communicated by C.S. Lin.
About this article
Cite this article
Fu, J., Wang, Z. & Wu, D. Form-type equations on Kähler manifolds of nonnegative orthogonal bisectional curvature. Calc. Var. 52, 327–344 (2015). https://doi.org/10.1007/s00526-014-0714-0