Thomas-Yau conjecture and holomorphic curves
Thomas-Yau conjecture and holomorphic curves
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托马斯-丘猜想和全纯曲线
DOI：
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发表时间：
2022
期刊：
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通讯作者：
Yang Li
中科院分区：
文献类型：
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作者：
Yang Li
本文的主题是丘-雅猜想，主要是在精确的，（定量）几乎校准，畅通无阻的拉格朗日膜内的卡拉比-丘斯坦流形的设置。在我们的解释中，猜想是，Mesquas-Yau半稳定性等价于特殊拉格朗日代表的存在。我们澄清如何全纯曲线进入这幅自然的图片，通过建设bordism电流之间的拉格朗日，并在定义的所罗门功能。在一些额外的假设下，我们将使用模空间上的积分技巧证明特殊拉格朗日量存在的Floer理论障碍。在匡威的方向上，我们建立了一个变分框架，目标是找到特殊的Lagrangian下的Mesquas-Yau半稳定性假设，我们将取得足够的进展，以查明突出的技术困难，无论是在Floer理论和几何测度理论。
The main theme of this paper is the Thomas-Yau conjecture, primarily in the setting of exact, (quantitatively) almost calibrated, unobstructed Lagrangian branes inside Calabi-Yau Stein manifolds. In our interpretation, the conjecture is that Thomas-Yau semistability is equivalent to the existence of special Lagrangian representatives. We clarify how holomorphic curves enter this conjectural picture, through the construction of bordism currents between Lagrangians, and in the definition of the Solomon functional. Under some extra hypothesis, we shall prove Floer theoretic obstructions to the existence of special Lagrangians, using the technique of integration over moduli spaces. In the converse direction, we set up a variational framework with the goal of finding special Lagrangians under the Thomas-Yau semistability asumption, and we shall make sufficient progress to pinpoint the outstanding technical difficulties, both in Floer theory and in geometric measure theory.