In this paper, the relationship between the existence of special lagrangian submanifolds and the collapsing of Calabi-Yau manifolds is studied. First, special lagrangian fibrations are constructed on some regions of bounded curvature and sufficiently collapsed in Ricci-flat Calabi-Yau manifolds. Then, in the opposite direction,it is shown that the existence of special lagrangian submanifolds with small volume implies the collapsing of some regions in the ambient Calabi-Yau manifolds.

中文翻译：

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Calabi-Yau 流形和特殊拉格朗日子流形的塌缩

本文研究了特殊拉格朗日子流形的存在与Calabi-Yau流形坍缩的关系。首先，特殊的拉格朗日纤维构造在一些有界曲率的区域上，并在 Ricci-flat Calabi-Yau 流形中充分坍缩。然后，在相反的方向上，表明小体积的特殊拉格朗日子流形的存在意味着周围 Calabi-Yau 流形中某些区域的坍塌。