[Authors] A. I. Nazarov, A. B. Reznikov [Title] Attainability of infima in the critical Sobolev trace embedding theorem on manifolds [AMS Subj-class] 49J10 Free problems in two or more independent variables 35J20 Variational methods for second-order, elliptic equations [Keywords] minimizers; trace Sobolev embedding; critical exponent; trace Sobolev--Poincar\'e inequality; $p$-Laplacian; optimal trace Sobolev inequality [Abstract] Sufficient conditions for the existence of extremal functions in the trace Sobolev inequality and the trace Sobolev--Poincar\'e inequality on Riemannian manifolds are established. It is shown that some of these conditions are sharp. [Comments] English, 15 pp. [Contact e-mail] al.il.nazarov@gmail.com