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 $M$.