A discrete four vertex theorem for hyperbolic polygons (Q6041850)

The classical four-vertex theorem in differential geometry states that the curvature along a simple closed smooth curve in the plane has at least four local extrema. There are several discrete versions of the four-vertex theorem. \textit{O. Musin} [``A four-vertex theorem for a polygon'', Kvant 2, 11--13 (1997)] introduced the notion of discrete curvature and proved a four-vertex theorem for Euclidean polygons. In [\textit{O. R. Musin}, J. Math. Sci., New York 119, No. 2, 268--277 (2001; Zbl 1077.51505); translation from Zap. Nauchn. Semin. POMI 280, 251--271 (2001)], he introduced the notion of discrete evolute. In the paper under review, the authors adapt the techniques of Musin and prove a discrete four-vertex theorem for convex hyperbolic polygons.