Timeline for Laplacian with singular potential
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 11, 2014 at 18:06 | answer | added | Graham Smith | timeline score: 1 | |
| Sep 3, 2014 at 20:10 | comment | added | Graham Smith | Indeed, you can use $r(x)=d(p,x)$, if you like... | |
| Sep 3, 2014 at 20:10 | comment | added | Graham Smith | The operator in question arises as the Jacobi operator of the Grimm Paraboloid, which is a complete, radially symmetric surface in $\Bbb{R}^3$ whose evolution under the mean curvature flow coincides with vertical translations. | |
| Sep 3, 2014 at 20:06 | comment | added | Graham Smith | I mean that I'm working in a conformal chart about $p$ which is biholomorphic to the Poincaré disk. The above formula is the expression for $L$ inside this chart. Alternatively, since I'm really only interested in understanding the behaviour of the operator near the singularity, you can think of the operator as acting on spaces of functions defined over the disk $\Bbb{D}$ and which vanish over the boundary. | |
| Sep 3, 2014 at 1:24 | comment | added | Richard Montgomery | What do you mean, r =|x|. Is not |x| =1 on the standard sphere?? Perhaps you mean $r(x) = dist_{S^2}(p, x)$? Where did this problem originate? | |
| Sep 2, 2014 at 20:50 | history | asked | Graham Smith | CC BY-SA 3.0 |