Symmetry problems on stationary isothermic surfaces in Euclidean spaces

Abstract

Let $S$ be a smooth hypersurface properly embedded in ${\mathbb{R}}^N$ with $N\ge 3$ and consider its tubular neighborhood $\mathcal{N}$. We show that, if a heat flow over $\mathcal{N}$ with appropriate initial and boundary conditions has $S$ as a stationary isothermic surface, then $S$ must have some sort of symmetry.

arXiv comment9 pages, to appear in Springer Proceedings in Mathematics & Statistics