Timeline for Uniqueness of a compatible Kahler-Einstein structure on a symplectic manifold?
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Jan 11, 2019 at 19:43 | vote | accept | Julian Chaidez | ||
| Dec 12, 2018 at 9:45 | history | edited | Ben McKay | CC BY-SA 4.0 |
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| Dec 12, 2018 at 9:38 | history | edited | Dmitri Panov | CC BY-SA 4.0 |
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| Dec 12, 2018 at 9:14 | comment | added | Dmitri Panov | Julian, concerning your second comment, what I wrote is different from Mostov rigidity. The claim is the following: if a complex 2-surface is homeomorphic to a ball quotient, then it is byholomorphic to it. Mostov rigidity is a statement about two ball quotients - if they have the same fundamental group they are isometric. But a priori one could imaging that there is a complex surface that is diffeomorphic to a ball quotient, but is not byholomorphic to a ball quotient. Yau's theorem rules this out. | |
| Dec 12, 2018 at 1:47 | comment | added | Julian Chaidez | For the case (iii), do you mean that the answer is positive for negative sectional curvature? If so, I think it might follow from Mostow- rigidity applied to the isometry group of the complex hyperbolic ball $\mathbb{B}^n$. This was actually my motivation for this question: mathoverflow.net/questions/317362/mostow-rigidity-for-complex-hyperbolic-manifolds. | |
| Dec 12, 2018 at 1:47 | comment | added | Julian Chaidez | Excellent, this is all very helpful. I probably should have thought about Questions 1 and 2 more before asking, Riemann surfaces seem to be a good source of counter-examples there. | |
| Dec 11, 2018 at 23:46 | history | answered | Dmitri Panov | CC BY-SA 4.0 |