论文标题
表面的锁定和解锁的平滑嵌入
Locked and unlocked smooth embeddings of surfaces
论文作者
论文摘要
我们研究了平面表面在三维欧几里得空间中平滑等轴测嵌入的连续运动，以及这些嵌入的两个相关的离散类似物，多边形嵌入和没有内部顶点的平坦折叠，在嵌入或折叠的连续变化下。我们表明，每个星形或螺旋形的域都被解锁：连续的运动将其展现到平坦的嵌入中。但是，带有两个孔的磁盘可能具有锁定的嵌入，这些嵌入在拓扑上等同于平坦的嵌入，但无法通过连续运动到达平坦的嵌入。
We study the continuous motion of smooth isometric embeddings of a planar surface in three-dimensional Euclidean space, and two related discrete analogues of these embeddings, polygonal embeddings and flat foldings without interior vertices, under continuous changes of the embedding or folding. We show that every star-shaped or spiral-shaped domain is unlocked: a continuous motion unfolds it to a flat embedding. However, disks with two holes can have locked embeddings that are topologically equivalent to a flat embedding but cannot reach a flat embedding by continuous motion.
