We study the Yamabe flow on a Riemannian manifold of dimension mβ₯3 minus
a closed submanifold of dimension n and prove that there exists an
instantaneously complete solution if and only if n>2mβ2β. In the
remaining cases 0β€nβ€2mβ2β including the borderline case, we
show that the removability of the n-dimensional singularity is necessarily
preserved along the Yamabe flow. In particular, the flow must remain
geodesically incomplete as long as it exists. This is contrasted with the
two-dimensional case, where instantaneously complete solutions always exist