Timeline for Do Laplace-Beltrami eigenfunctions vary continuously with the metric?
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 3, 2021 at 11:51 | vote | accept | Qualearn | ||
| Sep 11, 2021 at 19:56 | history | edited | Deane Yang | CC BY-SA 4.0 |
added 101 characters in body
|
| Sep 11, 2021 at 19:55 | comment | added | Deane Yang | @TerryTao, yes. When I said $C$ depends on $g_1$, I did have the reciprocal of the spectral gap in mind. But I see that I should say that $C$ depends on $g_1$ and $\lambda_1$. | |
| Sep 11, 2021 at 19:48 | comment | added | Terry Tao | The constant $C$ here will also depend on the invertibility of $-\Delta_1 + \lambda_1$ on the orthogonal complement of the kernel, hence depends on the spectral gap between $\lambda_1$ and the other eigenvalues of $-\Delta_1$. This is necessary, since if there were two eigenvalues $\lambda_1, \lambda'_1$ of $-\Delta_1$ close to $\lambda_2$ then your estimate would also imply that a $\lambda_1$-eigenfunction is close to a $\lambda'_1$-eigenfunction, contradicting orthogonality. | |
| Sep 11, 2021 at 18:48 | history | edited | Deane Yang | CC BY-SA 4.0 |
deleted 52 characters in body
|
| Sep 11, 2021 at 18:40 | history | answered | Deane Yang | CC BY-SA 4.0 |