The stationarity of the surface tension of ground state and heated symmetric semi-infinite nuclear matter with respect to density changes in the bulk phases

We present general proofs for the stationarity of the surface tension of symmetric semi-infinite nuclear matter, for the ground state as well as for T>0 states, metastable or in phase equilibrium with an external nucleon gas. This so-called 'dsigma=0' theorem is argued to be mathematical, derivable directly from the equilibrium of the bulk phases and the stationarity of the surface tension for density changes in the surface region. It is shown to be useful to test the accuracy of approximative and numerical procedures. (orig.)