论文标题
一组不稳定的曲线，用于在表面上变形的Hermitian Yang-Mills和Z-Critional方程
The set of destabilizing curves for deformed Hermitian Yang-Mills and Z-critical equations on surfaces
论文作者
论文摘要
我们表明，在任何紧凑的kähler表面存在上，可以使用有限数量的有效条件来表征z临界方程的溶液，其中条件的数量在上面的表面数量上以上是表面的Picard数量，这导致了Bridgeland稳定性中局部有限的壁chamber demopition的第一个PDE类似物。 作为应用程序，我们表征了唐纳森（Donaldson）的J-方程式和变形的Hermitian Yang-Mills方程式的最佳稳定曲线，这证明了对均匀J稳定性的最佳稳定测试配置的不存在结果，以及针对某些几何学流的改进结果进行评论。
We show that on any compact Kähler surface existence of solutions to the Z-critical equation can be characterized using a finite number of effective conditions, where the number of conditions is bounded above by the Picard number of the surface.This leads to a first PDE analogue of the locally finite wall-chamber decomposition in Bridgeland stability. As an application we characterize optimally destabilizing curves for Donaldson's J-equation and the deformed Hermitian Yang-Mills equation, prove a non-existence result for optimally destabilizing test configurations for uniform J-stability, and remark on improvements to convergence results for certain geometric flows.
