English

Energy properness and Sasakian-Einstein metrics

Differential Geometry 2011-07-21 v1

Abstract

In this paper, we show that the existence of Sasakian-Einstein metrics is closely related to the properness of corresponding energy functionals. Under the condition that admitting no nontrivial Hamiltonian holomorphic vector field, we prove that the existence of Sasakian-Einstein metric implies a Moser-Trudinger type inequality. At the end of this paper, we also obtain a Miyaoka-Yau type inequality in Sasakian geometry.

Keywords

Cite

@article{arxiv.1007.2626,
  title  = {Energy properness and Sasakian-Einstein metrics},
  author = {Xi Zhang},
  journal= {arXiv preprint arXiv:1007.2626},
  year   = {2011}
}

Comments

27 pages

R2 v1 2026-06-21T15:48:36.794Z