AI 中文总结
本文探究迈斯纳多面体的悬点是否影响表面积极小化，证明删除悬点不增最小表面积、添加悬点不减最小表面积，将面积极小化迈斯纳多面体的搜索简化为不含悬点的生成集。
AI 中文摘要
迈斯纳多面体是由单位直径的极值有限集得到的常宽体，这类生成集可能包含悬点，即仅有两个直径邻点的点。本文研究这些点是否能在表面积极小化中发挥重要作用：给定一个极值集，证明基于该集的迈斯纳多面体的最小表面积不会因删除一个悬点而增加；添加一个悬点无法减小可达到的最小表面积。这将面积极小化迈斯纳多面体的搜索简化为不含悬点的生成集。
英文摘要
Meissner polyhedra are constant-width bodies obtained from extremal finite sets of unit diameter. Such a generating set may contain dangling points, namely points having exactly two diametric neighbors. This article studies whether these points can play an essential role in surface-area minimization. Given an extremal set we show that the smallest surface area among the Meissner polyhedra based on it cannot increase by deleting a dangling point. Adding a dangling point cannot decrease the smallest achievable surface area. This reduces the search for area-minimizing Meissner polyhedra to generating sets without dangling points.
