Abstract
Let M 3 be a three-manifold (possibly with boundary). We will show that, for any positive integer γ, there exists an open nonempty set of metrics on M (in the C 2-topology on the space of metrics on M) for each of which there are compact embedded stable minimal surfaces of genus γ with arbitrarily large area. This extends a result of Colding and Minicozzi, who proved the case γ=1.
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