The käahler-ricci flow and the ¯ ∂ operator on vector fields

D.H. Phong Columbia University, New York Jian Song Johns Hopkins University, Baltimore Jacob Sturm Rutgers University, Newark Ben Weinkove Harvard University

Differential Geometry mathscidoc:1609.10109

Journal of Differential Geometry, 81, (3), 631-647, 2009
The limiting behavior of the normalized KÄahler-Ricci °ow for manifolds with positive ¯rst Chern class is examined under certain stability conditions. First, it is shown that if the Mabuchi Kenergy is bounded from below, then the scalar curvature converges uniformly to a constant. Second, it is shown that if the Mabuchi Kenergy is bounded from below and if the lowest positive eigenvalue of the ¹@y ¹@ operator on smooth vector ¯elds is bounded away from0 along the °ow, then the metrics converge exponentially fast in C1 to a KÄahler-Einstein metric.
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@inproceedings{d.h.2009the,
  title={THE KÄAHLER-RICCI FLOW AND THE ¯ ∂ OPERATOR ON VECTOR FIELDS},
  author={D.H. Phong, Jian Song, Jacob Sturm, and Ben Weinkove},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160911181412666690766},
  booktitle={Journal of Differential Geometry},
  volume={81},
  number={3},
  pages={631-647},
  year={2009},
}
D.H. Phong, Jian Song, Jacob Sturm, and Ben Weinkove. THE KÄAHLER-RICCI FLOW AND THE ¯ ∂ OPERATOR ON VECTOR FIELDS. 2009. Vol. 81. In Journal of Differential Geometry. pp.631-647. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160911181412666690766.
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