Timeline for Liouville property of hyperbolic spaces
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 24, 2022 at 9:39 | answer | added | R W | timeline score: 2 | |
| Feb 9, 2022 at 18:21 | comment | added | Moishe Kohan | The most direct proof is to use the conformal unit ball model and check that a coordinate function is harmonic (if you know the definition of harmonicity, this will be immediate). | |
| Feb 9, 2022 at 17:02 | comment | added | Neal | Realize $\mathbb{H}^n$ as the unit ball endowed with the hyperbolic metric. A function on the unit ball is harmonic with respect to the hyperbolic metric iff it is harmonic with respect to the Euclidean metric. So you can get harmonic functions on $\mathbb{H}^n$ by integrating a function on the boundary of the unit ball against the Poisson kernel. | |
| Feb 9, 2022 at 16:09 | history | edited | YCor |
edited tags
|
|
| Feb 9, 2022 at 15:58 | history | asked | SMS | CC BY-SA 4.0 |