Timeline for Finding a hyperbolic metric with geodesic boundary on a given Riemann surface
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
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| May 10, 2023 at 16:30 | comment | added | Yuxiao Xie | @MoisheKohan I don't understand why my question was in the differential category. I work on a given Riemann surface and I only consider conformal metrics on it. | |
| May 10, 2023 at 15:23 | comment | added | Moishe Kohan | @YuxiaoXie: You are wrong (confusing different categories: Your question was in differential geometry category and now you are switching to a related, but different category of bordered Riemann surfaces). | |
| May 10, 2023 at 7:23 | comment | added | Yuxiao Xie | But analyticity of the boundary is necessary. Consider, e.g., a pair of pants. If every pair of pants admits such a metric, then they would be isomorphic to a standard hyperbolic pair of pants, which already has analytic boundary. I guess a more precise way of stating what I'm looking for is that the hyperbolic metric should extend to a hyperbolic metric in a neighborhood of $X$ (after embedding $X$ in an open Riemann surface). | |
| May 10, 2023 at 0:28 | history | answered | Jeffrey Case | CC BY-SA 4.0 |