The Hermitian curvature flow on manifolds with non-negative Griffiths curvature

@article{Ustinovskiy2019TheHC,
  title={The Hermitian curvature flow on manifolds with non-negative Griffiths curvature},
  author={Yury Ustinovskiy},
  journal={American Journal of Mathematics},
  year={2019},
  volume={141},
  pages={1751 - 1775}
}
  • Yury Ustinovskiy
  • Published 17 April 2016
  • Mathematics
  • American Journal of Mathematics
Abstract:In this paper we study a particular version of the {\it Hermitian curvature flow} (HCF) over a compact complex Hermitian manifold $(M,g,J)$. We prove that if the initial metric has Griffiths positive (non-negative) Chern curvature $\Omega$, then this property is preserved along the flow. On a manifold with Griffiths non-negative Chern curvature the HCF has nice regularization properties, in particular, for any $t>0$ the zero set of $\Omega(\xi,\bar\xi,\eta,\bar\eta)$ becomes invariant… 
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