Timeline for Any papers on the "priori estimate approach" for Yamabe problem
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 7 at 12:47 | comment | added | Deane Yang | There is also the heat flow approach, which was actually carried out by Brendle. en.wikipedia.org/wiki/Yamabe_flow | |
| Nov 7 at 5:56 | comment | added | Elio Li | Thanks for your comment! maybe I didn't express my question clearly or my question is too naive, I mean that is there papers trying to solve the equation without treating the solution as the critical point of the functional, for example, using the continuity method you mentioned (the estimate for each order of the solution). | |
| Nov 6 at 16:21 | comment | added | Deane Yang | The variational approach does require a priori estimates. Another approach commonly used to prove the existence of solutions to a nonlinear PDE is the continuity method. For solutions that don’t minimize the Yamabe functional, one could try Morse theoretic approaches. All of the approaches require a priori estimates. | |
| Nov 6 at 14:54 | history | asked | Elio Li | CC BY-SA 4.0 |