Matzoh Ball Soup: Heat Conductors with a Stationary Isothermic Surface
Rolando Magnanini, Shigeru Sakaguchi · Annals of Mathematics · 2002
We consider a bounded heat conductor that satisfies the exterior sphere condition. Suppose that, initially, the conductor has temperature 0 and, at all times, its boundary is kept at temperature 1. We show that if the conductor contains a proper sub-domain, satisfying the interior cone condition and having constant boundary temperature at each given time, then the conductor must be a ball.