Timeline for Converting equation on the sphere to $\mathbb{R}^n$
Current License: CC BY-SA 4.0
7 events
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Nov 30, 2021 at 11:09 | history | edited | Student | CC BY-SA 4.0 |
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Nov 28, 2021 at 22:27 | history | edited | Student | CC BY-SA 4.0 |
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Nov 28, 2021 at 20:37 | comment | added | Student | @WillieWong thanks for the reference! I used the expression suggested there. Does the final expression look correct now? | |
Nov 28, 2021 at 13:11 | history | edited | Student | CC BY-SA 4.0 |
added 147 characters in body
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Nov 24, 2021 at 14:09 | comment | added | Willie Wong | The sphere metric is conformal to the flat metric. Which means that up to a scalar curvature term you can obtain one from conjugating the other against the conformal weight. See math.stackexchange.com/questions/3305797/… for some of the computations. (Specifically: see equation (1) in the question statement.) | |
Nov 24, 2021 at 12:53 | comment | added | username | As in $$\text{div}\left(\left(1+\left|x\right|^{2}\right)^{4-2n}\nabla\phi\right)+4\left(1+\left|x\right|^{2}\right)^{2-2n}\phi=0$$ you mean? I don't know if your formula is correct, but that's a self adjoint version of it. | |
Nov 24, 2021 at 12:27 | history | asked | Student | CC BY-SA 4.0 |