Symmetry problems on stationary isothermic surfaces in Euclidean spaces
Abstract
Let $S$ be a smooth hypersurface properly embedded in $\mathbb R^N$ with $N \geq 3$ 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.
 Publication:

arXiv eprints
 Pub Date:
 January 2016
 arXiv:
 arXiv:1601.01097
 Bibcode:
 2016arXiv160101097S
 Keywords:

 Mathematics  Analysis of PDEs
 EPrint:
 9 pages, to appear in Springer Proceedings in Mathematics &