Let Σ be a k-dimensional minimal submanifold in the n-dimensional unit ball Bn which passes through a point y∈ Bn and satisfies ∂Σ ⊂ ∂Bn. We show that the k-dimensional area of Σ is bounded from below by |Bk|(1-|y|2)k2. This settles a question left open by the work of Alexander and Osserman in 1973.
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