# 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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