CURVATURE-FREE ESTIMATES FOR THE SMALLEST AREA OF A MINIMAL SURFACE

REGINA ROTMAN ALEXANDER NABUTOVSKY

Abstract. In this paper we will present two upper estimates for the smallest area of a possibly singular minimal surface in a closed Riemannian manifold M^{n} with a trivial first homology group. The first upper bound will be in terms of the diameter of M^{n}, the second estimate will be in terms of the filling radius of a manifold, leading also to the estimate in terms of the volume of M^{n}. After that we will establish similar upper bounds for the smallest volume of a stationary k-dimensional integral varifold in a closed Riemannian manifold M^{n} with H_{1}(M^{n}) = ... = H_{k−1}(M^{n}) = {0}, (k > 2). The above results are the first results of such nature.