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Convex surfaces with prescribed induced metrics in anti-de Sitter spacetimes (2405.01912v1)
Published 3 May 2024 in math.DG and math.GT
Abstract: Let $S$ be a closed surface of genus at least $2$, let $h$ be a smooth metric of curvature $K<-1$ on $S$, and let $h_0$ be a hyperbolic metric on $S$. We show that there exists a unique quasifuchsian AdS spacetime with left metric isotopic to $h_0$, containing a past-convex Cauchy surface with induced metric isotopic to $h$.
- Notes on: “Lorentz spacetimes of constant curvature” [Geom. Dedicata 126 (2007), 3–45; mr2328921] by G. Mess. Geom. Dedicata, 126:47–70, 2007.
- Some open questions on anti-de sitter geometry. Arxiv preprint arXiv:1205.6103, 2012.
- Prescribing Gauss curvature of surfaces in 3-dimensional spacetimes, application to the Minkowski problem in Minkowski space. Ann. Inst. Fourier (Grenoble), 61(1):511–591, 2011.
- Global Lorentzian geometry, volume 202 of Monographs and Textbooks in Pure and Applied Mathematics. Marcel Dekker Inc., New York, second edition, 1996.
- A cyclic extension of the earthquake flow I. Geom. Topol., 17(1):157–234, 2013.
- A cyclic extension of the earthquake flow II. Ann. Sci. Éc. Norm. Supér. (4), 48(4):811–859, 2015.
- AdS manifolds with particles and earthquakes on singular surfaces. Geom. Funct. Anal., 19(1):41–82, 2009.
- Anti-de sitter geometry and teichmüller theory. In A. Papadopoulos K. Ohshika, editor, In the Tradition of Thurston, pages 545–643. Springer, 2020.
- Global aspects of the Cauchy problem in general relativity. Comm. Math. Phys., 14:329–335, 1969.
- Projective structures, grafting and measured laminations. Geom. Topol., 12(1):351–386, 2008.
- W. M. Goldman. Geometric structures on manifolds and varieties of representations. Contemporary Math., 74:168–198, 1988.
- Steven P. Kerckhoff. The Nielsen realization problem. Ann. of Math. (2), 117(2):235–265, 1983.
- Circle packings on surfaces with projective structures. J. Differential Geom., 63(3):349–397, 2003.
- Circle packings on surfaces with projective structures: a survey. In Spaces of Kleinian groups, volume 329 of London Math. Soc. Lecture Note Ser., pages 337–353. Cambridge Univ. Press, Cambridge, 2006.
- Circle packings on surfaces with projective structures and uniformization. Pacific J. Math., 225(2):287–300, 2006.
- Minimal surfaces and particles in 3-manifolds. Geom. Dedicata, 126:187–254, 2007.
- Geoffrey Mess. Lorentz spacetimes of constant curvature. Geom. Dedicata, 126:3–45, 2007.
- Length functions in teichmüller and anti-de sitter geometry. Forum of Mathematics, Sigma, 11:e101, 2023.
- Jean-Marc Schlenker. On the weyl problem for complete surfaces in the hyperbolic and anti-de sitter spaces, 2020.
- The grafting map of Teichmüller space. J. Amer. Math. Soc., 15(4):893–927 (electronic), 2002.
- J.-M. Schlenker and A. Yarmola. Properness for circle packings and Delaunay circle patterns on complex projective structures. ArXiv e-prints, June 2018.
- Andrea Tamburelli. Prescribing metrics on the boundary of anti–de Sitter 3-manifolds. Int. Math. Res. Not. IMRN, (5):1281–1313, 2018.
- W. P. Thurston. Earthquakes in 2-dimensional hyperbolic geometry. In Fundamentals of hyperbolic geometry: selected expositions, volume 328 of London Math. Soc. Lecture Note Ser., pages 267–289. Cambridge Univ. Press, Cambridge, 2006.
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