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A counterexample to Yau's bounded-mean-curvature embedding question
Yau asked whether every complete Riemannian manifold with bounded Ricci curvature and positive injectivity radius admits an isometric embedding into some Euclidean space with bounded mean curvature. We construct a counterexample: a smooth complete metric on $\mathbb{R}^4$ with bounded Ricci curvatur
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