Stationary isothermic surfaces for unbounded domains Rolando MagnaniniShigeru Sakaguchi 35K0535K2035J05stationary surfacesisoparametric surfacesoverdetermined problems The initial temperature of a heat conductor is zero and its boundary temperature is kept equal to one at each time. The conductor contains a stationary isothermic surface, that is, an invariant spatial level surface of the temperature. In a previous paper, we proved that, if the conductor is bounded, then it must be a ball. Here, we prove that the boundary of the conductor is either a hyperplane or the union of two parallel hyperplanes when it is unbounded and satisfies certain global assumptions. Indiana University Mathematics Journal 2007 text pdf 10.1512/iumj.2007.56.3150 10.1512/iumj.2007.56.3150 en Indiana Univ. Math. J. 56 (2007) 2723 - 2738 state-of-the-art mathematics http://iumj.org/access/