An upper bound for the smallest area of a minimal surface in manifolds of dimension four

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In this paper, we prove that for any closed 4-dimensional Riemannian manifold M with trivial first homology group, if the Ricci curvature |Ric|≤3, the diameter diam(M)≤ D and the volume vol(M)>v>0, then the area of a smallest 2-dimensional stationary integral varifold in M is bounded by F(v,D), for some function F that only depends on v and D. Our bound for the area is based on the estimation of the first homological filling function of M.