dg.differential geometry – The convex hull of a manifold whose cobordism class is trivial Answer

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dg.differential geometry – The convex hull of a manifold whose cobordism class is trivial

let $M$ be a compact orientable $n$ dimensional manifold. Assume that $M$ has trivial cobordism class. Is there an embedding of $M$ in some Euclidean space $\mathbb{R}^m$ such that the convex hull of $M$ is a $n+1$ dimensional manifold whose boundary is $M$.

Here the image of $M$ under the embedding is denoted again by $M$.

Grade: One can pose the same question in the following geometric manner:

Let M be a compact Riemannian manifold with trivial cobordism class. Is there an isometric embedding of $M$ in some Euclidean space such that the convex hull of $M$ is a manifold whose boundary is $M$.

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