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Asymptotically Poincare surfaces in quasi-Fuchsian manifolds.
- Source :
-
Proceedings of the American Mathematical Society . Mar2020, Vol. 148 Issue 3, p1239-1253. 15p. - Publication Year :
- 2020
-
Abstract
- We introduce the notion of an asymptotically Poincaré family of surfaces in an end of a quasi-Fuchsian manifold. We show that any such family gives a foliation of an end by asymptotically parallel convex surfaces, and that the asymptotic behavior of the first and second fundamental forms determines the projective structure at infinity. As an application, we establish a conjecture of Labourie from [J. London Math. Soc. 45 (1992), pp. 549-565] regarding constant Gaussian curvature surfaces. We also derive consequences for constant mean curvature surfaces. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00029939
- Volume :
- 148
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- Proceedings of the American Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 141437887
- Full Text :
- https://doi.org/10.1090/proc/14850