Timeline for Analogy of Liouville conformal mapping theorem with Mostow rigidity?
Current License: CC BY-SA 2.5
4 events
| when toggle format | what | by | license | comment | |
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| Jan 6, 2018 at 17:20 | vote | accept | macbeth | ||
| Mar 28, 2010 at 12:36 | comment | added | Benoît Kloeckner | You're right, and in a sense the flexibility of lower dimensional cases seem different: in the conformal case, it comes from the analogy between conformality and holomorphy, while in the hyperbolic case the point is that the boundary is a circle, and has therefore very few structure (any diffemorphism is conformal!). There are many other situation where the lower dimensional cases lack rigidity: think of Poincaré's conjecture for instance, or of the fundamental theorem of affine geometry (a transformation that preserves alignment is affine as soon as the dimension is at least 2). | |
| Mar 27, 2010 at 22:00 | comment | added | macbeth | +1 Thanks for the thoughts. I'm aware of the "quasi-conformal" standard proof of Mostow rigidity. But, as you say, this doesn't seem to explain the connection in dim-2 floppiness/ higher-dim rigidity that intrigues me. If nothing else, the boundary of the universal cover, where the conformal phenomena occur, will have dimension one less than the universal cover itself, where the hyperbolic phenomena occur. | |
| Mar 27, 2010 at 20:34 | history | answered | Benoît Kloeckner | CC BY-SA 2.5 |