We review first how properties of curved surfaces can be studied using Hill's thermodynamics, also called nano-thermodynamics. We proceed to show for the first time that Hill's analysis is equivalent to Gibbs analysis for surfaces of constant curvatures (cylinders or spheres). This simplifies the study of such surfaces on the nano-scale, and opens up a possibility to study non-equilibrium systems in a systematic manner. (C) 2018 Elsevier B.V. All rights reserved.