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Pinching of manifolds with negative curvature, following M. Gromov and W. Thurston. (Pincement des variétés à coubure négative d’après M. Gromov et W. Thurston.) (French) Zbl 1066.53509
Seminar on spectral theory and geometry, 1985-1986. Chambéry: Univ. de Savoie, Fac. des Sciences, Service de Math.; St. Martin d’Hères: Univ. de Grenoble I, Inst. Fourier. Sémin. Théor. Spectrale Géom., Chambéry-Grenoble 4, 101-113 (1986).
From the text: The object of this exposé is to make explicit parts of the following theorem due to M. Gromov and W. Thurston [Invent. Math. 89, 1–12 (1987; Zbl 0646.53037)]. Theorem: For all $$n \geq 4$$ and $$\delta > 0$$, there exists a compact manifold of dimension $$n$$ with a metric of negative curvature which does not carry a metric with curvature pinched between $$-1$$ and $$-\delta$$.
The parts discussed are the construction of constant curvature manifolds which admit ramified coverings, the construction of metrics of variable negative curvature on them, and the reason why these manifolds do not admit constant curvature metrics.
For the entire collection see [Zbl 0825.00039].

##### MSC:
 53C20 Global Riemannian geometry, including pinching
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