  In a remarkable article published in 1982, M. Gromov introduced the concept
of minimal volume, namely, the minimal volume of a manifold $M^n$ is defined to
be the greatest lower bound of the total volumes of $M^n$ with respect to
complete Riemannian metrics whose sectional curvature is bounded above in
absolute value by 1. While the minimal curvature, introduced by G. Yun in 1996,
is the smallest pinching of the sectional curvature among metrics of volume 1.
The goal of this article is to provide estimates to minimal volume and minimal
curvature on 4-dimensional compact manifolds involving some differential and
topological invariants. Among these ones, we get some sharp estimates for
minimal curvature.
