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In this paper we present upper bounds on the minimal mass of a non-trivial stationary 1-cycle. The results that we obtain are valid for all closed Riemannian manifolds. The first result is that the minimal mass of a stationary 1-cycle on a closed n-dimensional Riemannian manifold M n is bounded from above by ( n + 2)! d/4, where d is the diameter of a manifold M n. The second result is that the minimal mass of a stationary 1-cycle on a closed Riemannian manifold M n is bounded from above by $$ (n+2)! \textrm{FillRad}(M^n) \leq (n+2)!(n+1) n^n \sqrt{(n+1)!}(\textrm{vol}(M^n))^{1/n} $$ where $$ \textrm{FillRad}(M^n) $$ where is the filling radius of a manifold, and $$ (\textrm{vol}(M^n)) $$ where is its volume.

Volume, diameter and the minimal mass of a stationary 1-cycle