Riemann moduli spaces are quantum ergodic. (English) Zbl 1517.32029
In this paper, quantum ergodicity is shown for Riemann moduli spaces with Weil-Petersson metric under some technical structural and analytic assumptions. Similar results are also obtained for some other singular spaces with ergodic geodesic flow.
Reviewer: Thomas B. Ward (Durham)
MSC:
| 32G15 | Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables) |
| 58J51 | Relations between spectral theory and ergodic theory, e.g., quantum unique ergodicity |
| 58C40 | Spectral theory; eigenvalue problems on manifolds |
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