Timeline for Holomorphic functions in almost-complex geometry
Current License: CC BY-SA 2.5
8 events
| when toggle format | what | by | license | comment | |
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| Dec 6, 2010 at 16:18 | vote | accept | Florin Belgun | ||
| Dec 1, 2010 at 14:21 | comment | added | Florin Belgun | Yes. This is the E. Hopf maximum principle from 1927 | |
| Dec 1, 2010 at 13:09 | history | edited | BS. | CC BY-SA 2.5 |
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| Dec 1, 2010 at 13:03 | comment | added | BS. | You are right that it is important that the operator vanishes on the constants (i.e. has "no order 0 part") to conclude a maximum principle from the principal symbol. | |
| Dec 1, 2010 at 12:51 | vote | accept | Florin Belgun | ||
| Dec 1, 2010 at 12:51 | |||||
| Dec 1, 2010 at 12:50 | comment | added | Florin Belgun | Right, so the answer is the maximum principle applied to an operator with the same principal symbol as the Laplacian (The difference is a first-order term coming from the brackets [X,JX] which are non-zero in general). About the local question, I agree that if there are n independent functions around a point (dim M=2n), then the J is integrable around that point. Probably, if the J satifies further restrictions (e.g, nearly Kähler in dimension 6), then the existence of ONE non-constant holomorphic function would already imply the integrability. But this is another question. | |
| Dec 1, 2010 at 11:35 | history | edited | BS. | CC BY-SA 2.5 |
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| Dec 1, 2010 at 11:28 | history | answered | BS. | CC BY-SA 2.5 |