On the existence of isoperimetric extremals of rotation and the non-existence of rotary diffeomorphisms

Abstract

In this paper we study the existence and the uniqueness of isoperimetric extremals of rotation on two-dimensional (pseudo-) Riemannian manifolds and on surfaces on Euclidean space. We find the new form of their equations which is easier than results by S. G. Leiko. He introduced the notion of rotary
diffeomorphisms. We prove that rotary mappings don’t exist.