论文标题
拉格朗日阶段运算符和针对切线拉格朗日相流的应用的棕褐色con弹性属性
Tan-concavity property for Lagrangian phase operators and applications to the tangent Lagrangian phase flow
论文作者
论文摘要
我们探索了Lagrangian阶段运算符的棕褐色，用于研究变形的Hermitian Yang-Mills（DHYM）指标。只要校准度量标准，这种新的物业就可以弥补拉格朗日相运算符的缺陷。作为一个应用程序，我们在几乎校准的$（1,1）$的空间上介绍了切线拉格朗日相流（TLPF），该$（1,1）$ - 适合Collins-Yau最近发现的DHYM指标的GIT框架。 TLPF具有一些特殊属性，这些特性对于线束平均曲率流（即拉格朗日式平均曲率流的镜像）。我们表明，从任何初始数据开始的TLPF均在所有积极时间内都存在。此外，我们表明，假设存在$ c $ -subsolution，TLPF顺利收敛到DHYM公制，这为最高分支中DHYM指标的存在提供了新的证明。
We explore the tan-concavity of the Lagrangian phase operator for the study of the deformed Hermitian Yang-Mills (dHYM) metrics. This new property compensates for the lack of concavity of the Lagrangian phase operator as long as the metric is almost calibrated. As an application, we introduce the tangent Lagrangian phase flow (TLPF) on the space of almost calibrated $(1,1)$-forms that fits into the GIT framework for dHYM metrics recently discovered by Collins-Yau. The TLPF has some special properties that are not seen for the line bundle mean curvature flow (i.e. the mirror of the Lagrangian mean curvature flow for graphs). We show that the TLPF starting from any initial data exists for all positive time. Moreover, we show that the TLPF converges smoothly to a dHYM metric assuming the existence of a $C$-subsolution, which gives a new proof for the existence of dHYM metrics in the highest branch.
