Inserted: 28 dec 2022
Last Updated: 28 dec 2022
Journal: Pure Appl. Funct. Anal.
In this survey paper we report our recent results concerning a notion of curvatures for irregular curves defined in Euclidean spaces or in Riemannian surfaces. Some of our ideas are inspired among the others by the work of Professor Yurii G. Reshetnyak and of the Russian school (especially A. D. Alexandrov), who e.g. pointed out the relevant notion of modulus of a curve, the properties of one sidedly smooth curves, and the role of integral geometric formulas for the rotation of spherical curves.