Earthquakes on Riemann surfaces and on measured geodesic laminations. (English) Zbl 0754.32010
The author’s summary: “Let \(S\) be a closed orientable surface of genus at least 2. We study its Teichmüller space \({\mathcal F}(S)\), namely the space of isotropy classes of conformal structures on \(S\). W. P. Thurston introduced a certain compactification of \({\mathcal F}(S)\) what he called the space of projective measured geodesic laminations. He also introduced some transformations of Teichmüller space, called earthquakes, which are intimately related to the geometry of \({\mathcal F}(S)\). A general problem is to understand which geometric properties of Teichmüller space subsist at infinity, on Thurston’s boundary. In particular, it is natural to ask whether earthquakes continuously extend at certain points of Thurston’s boundary, and at precisely which points they do so. This is the principal question addressed in this paper”.
Reviewer: V.Z.Enol’skij (Kiev)
MSC:
| 32G15 | Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables) |
| 30F60 | Teichmüller theory for Riemann surfaces |
| 57M05 | Fundamental group, presentations, free differential calculus |
| 86A17 | Global dynamics, earthquake problems (MSC2010) |
Keywords:
Teichmüller space; space of projective measured geodesic laminations; transformations; earthquakes; Thurston’s boundaryReferences:
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