I have seen many PDE people work on the circle. It seems like such a common domain, sometimes even more common than on $\Bbb{R}$. Why? Does it just mean "some interval"? Why not just say an interval?
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$S^1$ typically denotes the circle, not the torus. – Guy Paterson-Jones Oct 20 '15 at 06:32
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1@GuyPaterson-Jones Of course a 1 dimensional torus is just a circle. :) But because you asked so nicely I'll change it to circle. – Oct 20 '15 at 06:33
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@GuyPaterson-Jones see https://en.wikipedia.org/wiki/Torus#n-dimensional_torus – Oct 20 '15 at 06:35
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Fair enough. I guess I'm stuck in 2-dimensional land when it comes to torii =P. – Guy Paterson-Jones Oct 20 '15 at 06:35
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It's simply a convenient way of saying that one is working on an interval with periodic boundary conditions.
Hans Lundmark
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