Timeline for Holomorphic maps from a Riemann surface of infinite genus
Current License: CC BY-SA 4.0
3 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 21, 2022 at 8:16 | comment | added | Moishe Kohan | @gaga: No, in Sam's example one cannot say this since $\pi_1(X\setminus K)$ is not normally generated by short loops (here $K$ is your compact subset). Also, I do not see why his $X$ cannot not carry a nonconstant bounded subharmonic function. | |
| Nov 21, 2022 at 6:04 | comment | added | gaga | Sam's idea and its generalization (Lemma 1) are very useful. By Lemma 1, any nonconstant holomorphic map from Sam's surface $X$ (with a minor modification?) to any closed hyperbolic Riemann surface can be lifted to the universal covering disc on the complement of some compact subset. This gives a nonconstant bounded subharmonic function on $X$, which seems to give a contradiction. | |
| Nov 21, 2022 at 1:57 | history | answered | Moishe Kohan | CC BY-SA 4.0 |