Evolutions of convex hulls and phase transitions in thermodynamics

The paper presents a classification of typical singularities of the equilibrium surface and the phase diagram of a twocomponent themodynamic mixture. The mathematical formulation of the problem describes the evolutions of the convex hulls of plane curves dependent on two parameters. There is a total of eight topologicalfy different evolutions.Translated from Itogi Nauki i Tekhniki, Seriya Sovermennye Problemy Matematiki, Noveishie Dostizheniya, Vol. 33, pp. 157–190, 1988.