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Jan 29, 2021 at 18:09 answer added Will Sawin timeline score: 4
Jan 29, 2021 at 12:18 vote accept biringer
Jan 29, 2021 at 9:30 answer added Moishe Kohan timeline score: 13
Jan 29, 2021 at 4:56 comment added Moishe Kohan Every nonorientable closed connected surface of negative Euler characteristic, admits a hyperbolic metric such that the surface is covered by 3 embedded disks.
Jan 29, 2021 at 2:57 comment added biringer I'm thinking open balls, although I doubt that matters, and yes, size the injectivity radius is allowed. (Pathwise isometrically embedded, i.e. Riemannianly embedded, not isometrically embedded.) But whatever, really. I initially thought this would be useful for something, but I'm not sure it is anymore. Thought it was curious enough to post though.
Jan 29, 2021 at 1:05 comment added Ian Agol Are your metric balls isometrically embedded in the surface? E.g., if I took a ball around a point of size the injectivity radius, would that be an embedded ball? And are the closed or open?
Jan 28, 2021 at 22:32 history edited biringer CC BY-SA 4.0
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Jan 28, 2021 at 20:41 comment added biringer Cool, good to know. 👍
Jan 28, 2021 at 20:06 comment added Will Sawin The surfaces in Theorem 1.10 of the linked paper, which I think is what you are referencing, are Hurwitz surfaces, which are always compact. For example this is because they are finitely tiled by a particular bounded hyperbolic triangle.
Jan 28, 2021 at 19:29 history asked biringer CC BY-SA 4.0