The Deformed Hermitian–Yang–Mills Equation in Geometry and Physics
The Deformed Hermitian–Yang–Mills Equation in Geometry and Physics
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DOI：
10.1093/oso/9780198802013.003.0004
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发表时间：
2017-12
期刊：
影响因子：
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通讯作者：
Tristan C. Collins;Dan Xie;S. Yau
中科院分区：
文献类型：
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作者：
Tristan C. Collins;Dan Xie;S. Yau
本章介绍了变形厄米-杨-米尔斯方程的数学和物理，这是Kähler流形上的一个完全非线性几何偏微分方程，在镜像对称中起着重要作用。本章讨论了方程的物理起源，以及最近的一些进展。另外，在3维空间中，证明了一个新的陈数不等式，并讨论了它与代数稳定性条件的关系。
This chapter provides an introduction to the mathematics and physics of the deformed Hermitian–Yang–Mills equation, a fully non-linear geometric PDE on Kähler manifolds, which plays an important role in mirror symmetry. The chapter discusses the physical origin of the equation, and some recent progress towards its solution. In addition, in dimension 3, it proves a new Chern number inequality and discusses the relationship with algebraic stability conditions.