论文标题
托马斯·尤（Thomas-Yau）的猜想和全态曲线
Thomas-Yau conjecture and holomorphic curves
论文作者
论文摘要
本文的主要主题是托马斯·尤（Thomas-Yau）的猜想，主要是在Calabi-yau Stein歧管内的精确（定量）几乎校准的，几乎经过校准的，几乎经过校准的，无障碍的Lagrangian Branes。在我们的解释中，猜想是，托马斯·考的可准性等效于特殊的拉格朗日代表的存在。我们通过在拉格朗日人之间的构造和所罗门功能的定义来阐明霍明态曲线如何进入这种猜想的情况。在一些额外的假设下，我们将利用模量空间的整合技术证明特殊拉格朗日人的存在理论障碍。在相反的方向上，我们建立了一个变异框架，目的是在托马斯·尤（Thomas-Yau）的可准性上找到特殊的拉格朗日人，并且在浮动理论和几何理论中，我们都将取得足够的进步来确定出色的技术困难。
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.
