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 $M$.

Note: 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 $M$?