Published November 2015
| Submitted
Journal Article
Open
The degeneration of convex ℝℙ^2 structures on surfaces
- Creators
- Zhang, Tengren
Abstract
Let M be a compact surface of negative Euler characteristic and let C(M) be the deformation space of convex real projective structures on M with positive hyperbolic holonomy. For every choice of pants decomposition for M, there is a well-known parameterization of C(M) known as the Goldman parameterization. In this paper, we study how some geometric properties of the real projective structure on M degenerate as we deform it so that the internal parameters of the Goldman parameterization leave every compact set, while the boundary invariants remain bounded away from zero and infinity.
Additional Information
© 2015 London Mathematical Society. Received 10 January 2014; revised 25 May 2015. The author was partially supported by NSF grant DMS-1006298. This work has benefitted from conversations with Gye-Seon Lee while he and the author were at the Center for Quantum Geometry of Moduli Spaces during August of 2013. The author also especially wishes to thank Richard Canary for introducing him to this subject, and the many fruitful discussions they have had in the course of writing this paper. Finally, the author is very grateful for the referee's careful reading of this paper and his/her many helpful comments.Attached Files
Submitted - 1312.2452v2.pdf
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1312.2452v2.pdf
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Additional details
- Eprint ID
- 64416
- DOI
- 10.1112/plms/pdv051
- Resolver ID
- CaltechAUTHORS:20160211-095235088
- NSF
- DMS-1006298
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2016-02-19Created from EPrint's datestamp field
- Updated
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2023-10-17Created from EPrint's last_modified field