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We prove the non‐existence of stable currents or compact stable minimal submanifolds for a class of submanifolds in a Euclidean space which satisfies an operative condition involving the Ricci curvature. In addition, we prove that these submanifolds are homeomorphic to the sphere. Moreover, we give examples which show that our result is optimal.
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Theodoros Vlachos (2004) studied this question.
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