Constant geodesic curvature curves and isoperimetric domains in rotationally symmetric surfaces (Q1599922)

Using methods of the calculus of variations, the author studies and classifies the closed embedded curves with constant geodesic curvature in some rotationally symmetric complete surfaces (planes, cylinders, spheres and projective planes). Furthermore, since the boundary curve \(\partial\Omega\) of an isopsrimetric domain \(\Omega\) on a Riemannian surface must be a closed embedded curve with constant geodesic curvature and especially a stable one, he applies his results in order to prove the existence or non-existence of isoperimetric domains. The latter are defined, when existent, and many interesting theorems are provided.