Timeline for Stability of bubbles under the heat flow
Current License: CC BY-SA 4.0
3 events
| when toggle format | what | by | license | comment | |
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| Apr 10, 2020 at 14:10 | comment | added | James Dibble | Thank you for the response. I do see from this that there is a singularity at $(x,T)$. I'm also concerned about the form of the singularity, though, and whether the bubbles converge to a bubble in the limit. I suspect they should. | |
| Apr 9, 2020 at 22:50 | comment | added | Otis Chodosh | Whenever you have monotonicity and epsilon regularity, the limit of singular points will be singular. If $X_j$ is singular, then epsilon regularity implies that $\Theta_{\Phi_k}(X_j)>\epsilon$ (where $\Theta$ is the monotone quantity: in this case, Struwe's quantity) so $\Theta_{\Phi_k}(X_j,r) >\epsilon$ for all $r>0$ by monotonicity. This passes to the limit, so $\Theta_{\Phi}(X,r)>\epsilon$ for all $r>0$. This implies that $X$ is a singular point. | |
| Apr 9, 2020 at 21:28 | history | asked | James Dibble | CC BY-SA 4.0 |