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首页> 外文期刊>Communications in Partial Differential Equations >Pluriclosed flow, Born-Infeld geometry, and rigidity results for generalized Kahler manifolds
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Pluriclosed flow, Born-Infeld geometry, and rigidity results for generalized Kahler manifolds

机译：广义Kahler流形的全封闭流，Born-Infeld几何和刚度结果

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摘要

We prove long time existence and convergence results for the pluriclosed flow, which imply geometric and topological classification theorems for generalized Kahler structures. Our approach centers on the reduction of pluriclosed flow to a degenerate parabolic equation for a (1, 0)-form, introduced in [30]. We observe a number of differential inequalities satisfied by this system which lead to a priori L estimates for the metric along the flow. Moreover we observe an unexpected connection to Born-Infeld geometry which leads to a sharp differential inequality which can be used to derive an Evans-Krylov type estimate for the degenerate parabolic system of equations. To show convergence of the flow we generalize Yau's oscillation estimate to the setting of generalized Kahler geometry.
机译：我们证明了多封闭流的长期存在和收敛结果，这暗示了广义Kahler结构的几何和拓扑分类定理。我们的方法集中在[30]中引入的将多闭环流简化为（1，0）形式的简并抛物线方程。我们观察到该系统满足的许多微分不等式，这些微分不等式导致沿流向度量的先验L估计。此外，我们观察到与Born-Infeld几何形状的意外连接，这导致了尖锐的微分不等式，可用于推导退化的抛物线方程组的Evans-Krylov类型估计。为了显示流的收敛性，我们将丘的振荡估计推广到广义Kahler几何的设置。

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