The paper of Michele Bartuccelli, Jonathan Deane and Sergey Zelik, entitled “Asymptotic expansions and extremals for the critical Sobolev and Gagliardo-Nirenberg inequalities on a torus” has been accepted for publication in the Proceedings of the Royal Society of Edinburgh.  The paper gives a comprehensive study of interpolation inequalities for periodic functions with zero mean, including the existence of and the asymptotic expansions for the extremals, best constants, various remainder terms and so on.  Most attention is paid to the critical (logarithmic) Sobolev inequality in the two-dimensional case, although a number of results concerning the best constants in the algebraic case and different space dimensions are also obtained.  An electronic copy of the final-form preprint is available here.