\indent Let $M_0$ be a closed subset of $R^n+1$ that is a smooth hypersurface except for a finite number of isolated singular points. Suppose that $M_0$ is asymptotic to a regular cone near each singular point. Can we flow $M_0$ by mean curvature? Theorem $(n<7)$: there exists a smooth mean curvature evolution starting at $M_0$ and defined for a short time $0