A generalization of the discrete isoperimetric inequality for piecewise smooth curves of constant geodesic curvature
In the geometries of constant curvature, the isoperimetric problem is well-known. That is, the maximal area polygon is regular if the number of vertices and its perimeter are given. In this article, the authors study its extension, considering polygons with circular arcs (with given radius) instead of polygons with geodesic edges. This is a kind of tickling problems in the plane geometry. Unfortunately the result is the same (that is, the regular polygon gives the maximal area.) Technically, they consider the configuration space with such circular polygons and solve the first derivatives.
scientific article; zbMATH DE number 5281484