多边形与多面体的曲率极值与四顶点定理
度量几何
2010-07-16 v3 组合数学
摘要
我们提出并发展了曲率极值的离散类比，以及四顶点定理向多边形和多面体情形的推广。对于平面中的光滑曲线和折线，我们得到了一个将曲率极值数目与曲线（折线）及其渐屈线的环绕数联系起来的公式。此外，还讨论了正则且可壳化的三角剖分的高维四顶点定理类比。
引用
@article{arxiv.0805.0629,
title = {Curvature extrema and four-vertex theorems for polygons and polyhedra},
author = {Oleg R. Musin},
journal= {arXiv preprint arXiv:0805.0629},
year = {2010}
}
备注
Several changes in the last section. In the original version of this paper we claimed that any regular triangulation of a convex d-polytope has at least d ears. For a proof we used the same arguments as in Schatteman's paper [22]. Since this paper has certain gaps (see our paper [1]), the d -ears problem of a regular triangulation is still open