We describe the lamination limits of sequences of compact disks \(M_n\) embedded in \({\mathbb {R}}^3\) with constant mean curvature \(H_n\), when the boundaries of these disks tend to infinity. This theorem generalizes to the non-zero constant mean curvature case Theorem 0.1 by Colding and Minicozzi (Ann Math 160:573–615, 2004) for minimal disks. We apply this theorem to prove the existence of a chord arc result for compact disks embedded in \({\mathbb {R}}^3\) with constant mean curvature; this chord arc result generalizes Theorem 0.5 by Colding and Minicozzi (Ann Math 167:211–243, 2008) for minimal disks.

当这些磁盘的边界趋于无穷大时，我们描述嵌入在\（{\ mathbb {R}} ^ 3 \）中的，具有恒定平均曲率\（H_n \）的压缩磁盘\（M_n \）的序列的层合极限。该定理通过最小化磁盘的Colding和Minicozzi（Ann Math 160：573–615，2004）推广到非零恒定平均曲率情况下的定理0.1。我们应用该定理证明了嵌入在具有平均曲率恒定的\（{{mathbb {R}} ^ 3 \）中的光盘的弦弧结果的存在；这个和弦弧的结果推广了Colding和Minicozzi的定理0.5（Ann Math 167：211–243，2008），用于最小圆盘。