Curvature extrema and four-vertex theorems for polygons and polyhedra

Details Curvature extrema and four-vertex theorems for polygons and polyhedra Curvature extrema and four-vertex theorems for polygons and polyhedra

2008-05-06

arxiv.org/abs/0805.0629v3

Journal of Mathematical Sciences, Vol. 119, No 2, 268-277, 2004

Mathematics

Metric Geometry

Several changes in the last section. In the original version of this paper we claimed that any regular triangulation of a conv

Scientific paper

Discrete analogs of extrema of curvature and generalizations of the four-vertex theorem to the case of polygons and polyhedra are suggested and developed. For smooth curves and polygonal lines in the plane, a formula relating the number of extrema of curvature to the winding numbers of the curves (polygonal lines) and their evolutes is obtained. Also are considered higher-dimensional analogs of the four-vertex theorem for regular and shellable triangulations.

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