Symmetry problems on stationary isothermic surfaces in Euclidean spaces

Shigeru Sakaguchi

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arXiv · 1601.01097

Symmetry problems on stationary isothermic surfaces in Euclidean spaces

Shigeru Sakaguchi

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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.

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Shigeru Sakaguchi. 2016-04-05. Symmetry problems on stationary isothermic surfaces in Euclidean spaces. https://arxiv.org/abs/1601.01097

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