Summary: We consider solutions of initial-boundary value problems for the heat equation on bounded domains in \(\mathbb{R}^N\), and their spatial critical points as in part I of this paper [J. Anal. Math. 71, 237-261 (1997; Zbl 0892.35010)]. In Dirichlet, Neumann, and Robin homogeneous initial-boundary value problems on bounded domains, it is proved that if the origin is a spatial critical point never moving for sufficiently many compactly supported initial data being centrosymmetric with respect to the origin, then the domain must be centrosymmetric with respect to the origin. Furthermore, we consider spatial zero points instead of spatial critical points, and prove some similar symmetry theorems. Also, it is proved that these symmetry theorems hold for initial-boundary value problems for the wave equation.
The Corrigendum [Zbl 01384395] concerns corrections of the proofs of Theorems 2 and 3.