Closed submanifolds in nonnegative k-Ricci manifolds with Euclidean volume growth satisfy the sharp inequality ∫|σ|^n ≥ θ|S^n|, with equality rigidity.
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Fenchel-Willmore inequality for submanifolds in manifolds with non-negative $k$-Ricci curvature
Closed submanifolds in nonnegative k-Ricci manifolds with Euclidean volume growth satisfy the sharp inequality ∫|σ|^n ≥ θ|S^n|, with equality rigidity.