Consider the following question: Does there exist a three-manifold M for which, given any riemannian metric on M there is an area bound for embedded minimal spheres? We answer this question negatively, and, in fact, find an open set of metrics for which this question is false. This generalizes similar results for surfaces of positive genus shown by W. Minicozzi, T. Colding and B. Dean. In addition, this paper provides some background on minimal surface theory related to the main theorem, as well as Colding and Minicozzi's proof for the torus. Some further directions for research are discussed in chapter 5.
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