We study the problem of finding neck-like features on a surface. Applications for such cuts include robotics, mesh segmentation, and algorithmic applications. We provide a new definition for a surface bottleneck -- informally, it is the shortest cycle relative to the size of the areas it separates. Inspired by the isoperimetric inequality, we formally define such optimal cuts, study their properties, and present several algorithms inspired by these ideas that work surprisingly well in practice. For examples of our algorithms, see https://neckcut.space.

翻译：本研究探讨在曲面上寻找颈部特征的问题。此类切割在机器人学、网格分割及算法应用中具有重要价值。我们提出了一种新的曲面瓶颈定义——直观而言，它是相对于所分隔区域尺寸的最短环路。受等周不等式启发，我们正式定义了此类最优切割，研究了其数学特性，并基于该理论提出了多种算法。实践表明这些算法具有优异的性能表现。算法示例详见 https://neckcut.space。