Abstract
We study the generalized Abreu equation in n-dimensional polytopes and derive some differential inequalities for homogeneous toric bundles.
Similar content being viewed by others
References
Arvanitoyeorgos, A.: An Introduction to Li Groups and the Geometry of Homogeneous Spaces. Translated from the 1999 Greek original and revised by the author, Student Mathematical Library, 22. American Mathematical Society, Providence (2003)
Chen, B., Li, A.-M., Sheng, L.: Uniform K-stability for extremal metrics on toric varieties. J. Differ. Equ. 257, 1487–1500 (2014)
Chen, B., Li, A.-M., Sheng, L.: Affine techniques on extremal metrics on toric surfaces. arXiv:1008.2606
Chen, B., Li, A.-M., Sheng, L.: Extremal metrics on toric surfaces. arXiv:1008.2607
Donaldson, S.K.: Scalar curvature and stability of toric varieties. J. Differ. Geom. 62, 289–349 (2002)
Donaldson, S.K.: Interior estimates for solutions of Abreu’s equation. Collect. Math. 56, 103–142 (2005)
Donaldson, S.K.: Extremal metrics on toric surfaces: a continuity method. J. Differ. Geom. 79, 389–432 (2008)
Donaldson, S.K.: Kähler Geometry on Toric Manifolds, and Some Other Manifolds with Large Symmetry. Handbook of Geometric Analysis, No. 1. International Press, Boston (2008)
Donaldson, S.K.: Constant scalar curvature metrics on toric surfaces. Geom. Funct. Anal. 19, 83–136 (2009)
Nyberg, T.: Constant scalar curvature of toric fibrations. PhD thesis
Podesta, F., Spiro, A.: Kähler–Ricci solitons on homogeneous toric bundles. J. Reine Angew. Math. 642, 109–127 (2010)
Raza, A.: Scalar curvature and multiplicity-free actions. PhD thesis
Author information
Authors and Affiliations
Corresponding author
Additional information
Li acknowledges the support of NSFC Grant 11521061. Sheng acknowledges the support of NSFC Grant 11471225. Zhao acknowledges the support of NSFC Grants 11571242.
Rights and permissions
About this article
Cite this article
Li, AM., Sheng, L. & Zhao, G. Differential inequalities on homogeneous toric bundles. J. Geom. 108, 775–790 (2017). https://doi.org/10.1007/s00022-017-0372-4
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00022-017-0372-4