A special Lagrangian type equation for holomorphic line bundles

Adam Jacob Shing-Tung Yau

Complex Variables and Complex Analysis mathscidoc:1912.43584

Mathematische Annalen, 369, 869-898, 2017.10
Let <i>L</i> be a holomorphic line bundle over a compact Khler manifold <i>X</i>. Motivated by mirror symmetry, we study the deformed HermitianYangMills equation on <i>L</i>, which is the line bundle analogue of the special Lagrangian equation in the case that <i>X</i> is CalabiYau. We show that this equation is the Euler-Lagrange equation for a positive functional, and that solutions are unique global minimizers. We provide a necessary and sufficient criterion for existence in the case that <i>X</i> is a Khler surface. For the higher dimensional cases, we introduce a line bundle version of the Lagrangian mean curvature flow, and prove convergence when <i>L</i> is ample and <i>X</i> has non-negative orthogonal bisectional curvature.
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  title={A special Lagrangian type equation for holomorphic line bundles},
  author={Adam Jacob, and Shing-Tung Yau},
  booktitle={Mathematische Annalen},
Adam Jacob, and Shing-Tung Yau. A special Lagrangian type equation for holomorphic line bundles. 2017. Vol. 369. In Mathematische Annalen. pp.869-898. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224204228996153148.
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