Shortest paths in arbitrary plane domains

L. C. Hoehn, L. G. Oversteegen, E. D. Tymchatyn

Let $\Omega$ be a connected open set in the plane and $\gamma :[0,1]\to \overline{\Omega }$ a path such that $\gamma ((0,1))\subset \Omega$. We show that the path $\gamma$ can be ``pulled tight'' to a unique shor…