论文标题
$ g_2 $ - 结构的流量与calabi-yau歧管相关
Flows of $G_2$-Structures associated to Calabi-Yau Manifolds
论文作者
论文摘要
我们建立了抛物线复杂的Monge-ampère方程与$ G_2 $ -LAPLACIAN流量之间的对应关系，用于从Kähler指标上产生的初始数据，该数据以复杂的$ 2 $ - 或$ 3 $ fold。通过应用对复杂的Monge-Ampère方程式的估计，我们表明，对于此类的初始数据，$ G_2 $ -LAPLACIAN流一直存在，并收集到由Kählerricci-flat衡量标准的无扭力$ G_2 $结构。对于$ G_2 $ -LAPLACIAN COFLOW，获得了类似的结果，在这种情况下，Coflow与Kähler-ricci流有关。
We establish a correspondence between a parabolic complex Monge-Ampère equation and the $G_2$-Laplacian flow for initial data produced from a Kähler metric on a complex $2$- or $3$-fold. By applying estimate for the complex Monge-Ampère equation, we show that for this class of initial data the $G_2$-Laplacian flow exists for all time and converges to a torsion-free $G_2$-structure induced by a Kähler Ricci-flat metric. Similar results are obtained for the $G_2$-Laplacian coflow, and in this case the coflow is related to the Kähler-Ricci flow.
