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- W4289693813 abstract "Let $S$ be a compact, orientable surface of hyperbolic type. Let $(k_+,k_-)$ be a pair of negative numbers and let $(g_+, g_-)$ be a pair of marked metrics over $S$ of constant curvature equal to $k_+$ and $k_-$ respectively. Using a functional introduced by Bonsante, Mondello & Schlenker, we show that there exists a unique affine deformation $Gamma:=(rho,tau)$ of a Fuchsian group such that $(S,g_+)$ and $(S, g_-)$ embed isometrically as locally strictly convex Cauchy surfaces in the future and past complete components respectively of the quotient by $Gamma$ of an open subset $Omega$ of Minkowski space. Such quotients are known as Globally Hyperbolic, Maximal, Cauchy compact Min-kow-ski spacetimes and are naturally dual to the half-pipe spaces introduced by Danciger. When translated into this latter framework, our result states that there exists a unique, marked, quasi-Fuchsian half-pipe space in which $(S, g_+)$ and $(S, g_-)$ are realised as the third fundamental forms of future- and past-oriented, locally strictly convex graphs." @default.
- W4289693813 created "2022-08-04" @default.
- W4289693813 creator A5025612386 @default.
- W4289693813 creator A5047941146 @default.
- W4289693813 date "2018-08-15" @default.
- W4289693813 modified "2023-10-14" @default.
- W4289693813 title "A note on invariant constant curvature immersions in Minkowski space" @default.
- W4289693813 doi "https://doi.org/10.48550/arxiv.1808.05201" @default.
- W4289693813 hasPublicationYear "2018" @default.
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