- #1

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Can someone please tell me what this smooth map is between them? I can only think of using the map (x,y) --> (sqrt(x), y) if x is non-negative and (sqrt(-x), y) if x is negative. Thanks for any help.

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- Thread starter Pip021
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- #1

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Can someone please tell me what this smooth map is between them? I can only think of using the map (x,y) --> (sqrt(x), y) if x is non-negative and (sqrt(-x), y) if x is negative. Thanks for any help.

- #2

HallsofIvy

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- #3

mathwonk

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is there a smoothness problem at x=0? (in answer #1)

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mathwonk

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An abstract approach is Riemann's mapping theorem, with extension to the boundary, that apparently gives an analytic map.

- #5

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mathwonk: I don't think there is a problem at x=0 (for Halls' map) because you can just define r to be 1 for x=0 and then it is smooth on S1.

- #6

mathwonk

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well you have prove it is smooth.

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