We obtain upper and lower bounds for the relative Gromov width of Lagrangian cobordisms between Legendrian submanifolds. Upper bounds arise from the existence of $J$-holomorphic disks with boundary on the Lagrangian cobordism that pass through the center of any given symplectically embedded ball. The areas of these disks --- and hence the sizes of these balls --- are controlled by a real-valued fundamental capacity, a quantity derived from the algebraic structure of filtered linearized Legendrian Contact Homology of the Legendrian at the top of the cobordism. Lower bounds come from explicit constructions that use neighborhoods of Reeb chords in the Legendrian ends. We also study relationships between the relative Gromov width and another quantitative measurement, the length of a Lagrangian cobordism.

中文翻译：

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Legendrians之间拉格朗日协边的相对格罗莫夫宽度

我们获得了勒格朗日子流形之间拉格朗日协边的相对格罗莫夫宽度的上限和下限。上界源于$J$-全纯圆盘的存在，该圆盘在通过任何给定辛嵌入球的中心的拉格朗日协边上具有边界。这些圆盘的面积 --- 以及这些球的大小 --- 由实值基本容量控制，该量从过滤线性化的Legendrian Contact Homology 的代数结构推导出来，在cobordism 的顶部. 下界来自在 Legendrian 端使用 Reeb 和弦邻域的显式构造。我们还研究了相对格罗莫夫宽度与另一个定量测量值之间的关系，即拉格朗日坐标的长度。