Skip to main content
Log in

Form-type equations on Kähler manifolds of nonnegative orthogonal bisectional curvature

  • Published:
Calculus of Variations and Partial Differential Equations Aims and scope Submit manuscript

Abstract

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, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Błocki, Z.: On uniform estimate in Calabi–Yau Theorem. Sci. China Ser. A Math. 48, 244–247 (2005)

    Article  MATH  Google Scholar 

  2. Fu, J.-X., Wang, Z., Wu, D.: Form-type Calabi–Yau equations. Math. Res. Lett. 17, 887–903 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  3. Gilbarg, D., Trudinger, N.: Elliptic Partial Differential Equations of Second order, Springer, Berlin, Paperback edition, (2001)

  4. Gu, H.-L., Zhang, Z.-H.: An extension of Mok’s Theorem on the generalized Frankel conjecture. Sci. China Math. 53, 1253–1264 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  5. Guan, B., Li, Q.: Complex Monge–Ampère equations and totally geodesic manifolds. Adv. Math. 225, 1185–1223 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  6. Han, Q., Lin, F.: Elliptic partial differential equations. In: Courant Lecture Notes in Mathematics, vol. 1, AMS Press, Brooklyn (2000)

  7. Mok, N.: The Uniformization theorem for compact Kähler manifolds of nonnegative holomorphic bisectional curvature. J. Differ. Geom. 27, 179–214 (1988)

    MATH  MathSciNet  Google Scholar 

  8. Siu, Y.-T., Yau, S.-T.: Complex Kähler manifolds of positive bisectional curvature. Invent. Math. 59, 189–204 (1980)

    Article  MATH  MathSciNet  Google Scholar 

  9. Tosatti, V., Weinkove, B.: The complex Monge–Ampère equation on compact Hermitian manifolds. J. Am. Math. Soc. 23, 1187–1195 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  10. 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)

    Article  MATH  Google Scholar 

Download references

Acknowledgments

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.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Jixiang Fu.

Additional information

Communicated by C.S. Lin.

Rights and permissions

Reprints and permissions

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

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00526-014-0714-0

Mathematics Subject Classification

Navigation