Timeline for Some questions on the nodal geometry of Dirac operators
Current License: CC BY-SA 3.0
5 events
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| Feb 9, 2016 at 8:41 | history | edited | SMS |
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| Feb 7, 2016 at 11:18 | comment | added | Sebastian Goette | I can think of a rather trivial example. Assume that $n=2$. Then the underlying manifold $M$ is a surface, and if it is orientable, then $S=S^+\oplus S^-$. Assume that $h$ anticommutes with the Clifford volume element, then $D+h\colon\Gamma(S^\pm)\to\Gamma(S^\mp)$. Sometimes, the index theorem forces $\ker(D+h)$ to be nontrivial either on $S^+$ or on $S^-$. If that bundle has nontrivial first Chern class, then every harmonic section must have $N_h\ne 0$. In fact $|c_1(S^\pm)[M]|$ is a lower bound on the number of zeros, which is the $0$-dimensional Hausdorff measure. | |
| S Feb 7, 2016 at 11:11 | history | suggested | Sebastian Goette | CC BY-SA 3.0 |
Hausdorff dimension replaced by Hausdorff measure
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| Feb 7, 2016 at 11:08 | review | Suggested edits | |||
| S Feb 7, 2016 at 11:11 | |||||
| Feb 7, 2016 at 9:51 | history | asked | SMS | CC BY-SA 3.0 |