Timeline for Eigenfunction on surface with boundary
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 5, 2014 at 17:19 | answer | added | Robert Bryant | timeline score: 3 | |
| Dec 5, 2014 at 14:45 | comment | added | Robert Bryant | @Slm2004: Ah! I see that I made a mistake in my calculations. You are right, the general solution in this particular case is $f = ax+by$ where $a$ and $b$ are constants, so there are two solutions, as you said. | |
| Dec 5, 2014 at 13:56 | comment | added | Slm2004 | @RobertBryant. Thank you for your attentiona. Yes. It does exist a nontrivial one when $M$ is the unit disk with Euclidean metric. Actually there are two linear independently solutions of the corresponding problem. Someone told me this is related to stelov eigenvalue problem. I am looking for the reference on it but have not known how to prove this yet. | |
| Dec 3, 2014 at 15:36 | comment | added | Robert Bryant | There is not a nonzero solution $f$ even when $M$ is the unit disk in the Euclidean plane (i.e., $K=0$, $\kappa = 1$), so it would appear that nontrivial solutions only exist in special cases. | |
| Dec 3, 2014 at 3:08 | comment | added | Igor Rivin | Why is there a solution if you drop the second condition? | |
| Dec 2, 2014 at 20:51 | history | asked | Slm2004 | CC BY-SA 3.0 |